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Questions and Answers
Transform the product $2 \cos 73^\circ \sin 62^\circ$ into a sum or difference of sines or cosines.
Transform the product $2 \cos 73^\circ \sin 62^\circ$ into a sum or difference of sines or cosines.
- $cos 135^\circ - sin 11^\circ$
- $sin 135^\circ - sin 11^\circ$ (correct)
- $cos 135^\circ - cos 11^\circ$
- $sin 135^\circ + cos 11^\circ$
Transform the product $2 \sin 41^\circ \cos 24^\circ$ into a sum or difference of sines or cosines.
Transform the product $2 \sin 41^\circ \cos 24^\circ$ into a sum or difference of sines or cosines.
- $cos 65^\circ - sin 17^\circ$
- $sin 65^\circ + cos 17^\circ$
- $cos 65^\circ - cos 17^\circ$
- $sin 65^\circ + sin 17^\circ$ (correct)
Transform the product $2 \cos 2^\circ \cos 3^\circ$ into a sum or difference of sines or cosines.
Transform the product $2 \cos 2^\circ \cos 3^\circ$ into a sum or difference of sines or cosines.
- $cos 5^\circ - cos 1^\circ$
- $cos 5^\circ + cos 1^\circ$ (correct)
- $sin 5^\circ + sin 1^\circ$
- $sin 5^\circ + cos 1^\circ$
Transform the product $2 \sin 29^\circ \sin 16^\circ$ into a sum or difference of sines or cosines.
Transform the product $2 \sin 29^\circ \sin 16^\circ$ into a sum or difference of sines or cosines.
$sin 2x = $
$sin 2x = $
$cos^2x = \frac{1+cos2x}{2}$. Name the property.
$cos^2x = \frac{1+cos2x}{2}$. Name the property.
sin x cos x = \frac{1}{2} sin 2x$. Name the property.
sin x cos x = \frac{1}{2} sin 2x$. Name the property.
If $cos x = 0.3$, find the exact value of $cos 2x$.
If $cos x = 0.3$, find the exact value of $cos 2x$.
$tan 2A = \frac{2 tan A}{1-tan^2A}$. Name the property.
$tan 2A = \frac{2 tan A}{1-tan^2A}$. Name the property.
$\cos(-x) = $
$\cos(-x) = $
In general, cos(x + y)= ................... in terms of cosines and sines of x and y.
In general, cos(x + y)= ................... in terms of cosines and sines of x and y.
Cos 7 cos 3 + sin 7 sin 3 =
Cos 7 cos 3 + sin 7 sin 3 =
$cos 2A = cos^2 A – sin^2 A$
$cos 2A = cos^2 A – sin^2 A$
$tan 2A = \frac{2 tan A}{1+tan^2A}$
$tan 2A = \frac{2 tan A}{1+tan^2A}$
$cos 2A = 2 cos^2 A + 1$
$cos 2A = 2 cos^2 A + 1$
$cos 2A = 1 + 2 sin^2 A$
$cos 2A = 1 + 2 sin^2 A$
$sin(-x) = sin x$
$sin(-x) = sin x$
Cosine and its reciprocal are even functions
Cosine and its reciprocal are even functions
$tan(-x) = tan(x)$
$tan(-x) = tan(x)$
$Cot (-x) = cot x$
$Cot (-x) = cot x$
Sine and its reciprocal are odd functions
Sine and its reciprocal are odd functions
$Sin (A + B) = sin A cos B + cos A sin B$
$Sin (A + B) = sin A cos B + cos A sin B$
Flashcards
Product-to-Sum Formulas
Product-to-Sum Formulas
Transforms a product of trigonometric functions into a sum or difference.
2cos(a)sin(b) Formula
2cos(a)sin(b) Formula
2cos(a)sin(b) = sin(a+b) - sin(a-b)
2sin(a)cos(b) Formula
2sin(a)cos(b) Formula
2sin(a)cos(b) = sin(a+b) + sin(a-b)
2cos(a)cos(b) Formula
2cos(a)cos(b) Formula
2cos(a)cos(b) = cos(a+b) + cos(a-b)
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2sin(a)sin(b) Formula
2sin(a)sin(b) Formula
2sin(a)sin(b) = cos(a-b) - cos(a+b)
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Double Angle Formula for Sine
Double Angle Formula for Sine
sin(2x) = 2sin(x)cos(x)
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Power-Reducing Formula for Cosine
Power-Reducing Formula for Cosine
cos²(x) = (1 + cos(2x))/2
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Power-Reducing Formula for Sine
Power-Reducing Formula for Sine
sin²(x) = (1 - cos(2x))/2
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Double Angle Formula for Cosine (Version 1)
Double Angle Formula for Cosine (Version 1)
cos(2x) = cos²(x) - sin²(x)
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Double Angle Formula for Cosine (Version 2)
Double Angle Formula for Cosine (Version 2)
cos(2x) = 2cos²(x) - 1
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Double Angle Formula for Cosine (Version 3)
Double Angle Formula for Cosine (Version 3)
cos(2x) = 1 - 2sin²(x)
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Double Angle Formula for Tangent
Double Angle Formula for Tangent
tan(2A) = (2tan(A))/(1 - tan²(A))
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Cosine of a Negative Angle
Cosine of a Negative Angle
cos(-x) = cos(x)
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Cosecant of a Negative Angle
Cosecant of a Negative Angle
csc(-x) = -csc(x)
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Cosine Sum Formula
Cosine Sum Formula
cos(x + y) = cos(x)cos(y) - sin(x)sin(y)
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Cosine Difference Formula
Cosine Difference Formula
cos(x - y) = cos(x)cos(y) + sin(x)sin(y)
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Sine of a Negative Angle
Sine of a Negative Angle
sin(-x) = -sin(x)
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Tangent of a Negative Angle
Tangent of a Negative Angle
tan(-x) = -tan(x)
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Cotangent of a Negative Angle
Cotangent of a Negative Angle
cot(-x) = -cot(x)
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Sine Sum Formula
Sine Sum Formula
sin(A + B) = sin A cos B + cos A sin B
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Even Function
Even Function
An even function satisfies f(-x) = f(x).
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Odd Function
Odd Function
An odd function satisfies f(-x) = -f(x).
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Even Trigonometric Functions
Even Trigonometric Functions
Cosine, Secant
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Odd Trigonometric Functions
Odd Trigonometric Functions
Sine, Tangent, Cosecant, Cotangent
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Sine Difference Formula
Sine Difference Formula
sin (A - B) = sin A cos B - cos A sin B
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Tangent Sum Formula
Tangent Sum Formula
tan (A + B) = (tan A + tan B) / (1 - tan A tan B)
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Tangent Difference Formula
Tangent Difference Formula
tan (A - B) = (tan A - tan B) / (1 + tan A tan B)
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Cosine Sum Formula
Cosine Sum Formula
cos (A + B) = cos A cos B - sin A sin B
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Cosine Difference Formula
Cosine Difference Formula
cos (A - B) = cos A cos B + sin A sin B
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Pythagorean Identity
Pythagorean Identity
sin²(x) + cos²(X) =1
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- The document is a Math worksheet for Grade 11 students, covering trigonometric identities and transformations.
Multiple Choice Questions:
- 2 cos 73° sin 62° can be transformed into sin 135° - sin 11°.
- 2 sin 41° cos 24° can be transformed into sin 65° + sin 17°.
- 2 cos 2° cos 3° can be transformed into cos 5° + cos 1°.
- 2 sin 29° sin 16° can be transformed into cos 13° - cos 45°.
- sin 2x = 2 sin x cos x
- cos²x = (1+cos2x)/2 is the Square of cosine property.
- sin²x = (1-cos2x)/2 is the Square of sine property.
- 2 sin x cos x = (1/2) sin 2x is the Product of sine and cosine property.
- If cos x = 0.3, the exact value of cos 2x is -0.82.
- tan 2A = (2 tan A)/(1-tan²A) is the Double Argument property for tan.
- cos(-x) = cos(x)
- cosec (-x) = - cosec(x)
- The general form of cos(x + y) in terms of cosines and sines of x and y is cos x cos y - sin x sin y.
- cos 7 cos 3 + sin 7 sin 3 = cos 4
- cos 7 cos 3 - sin 7 sin 3 = cos 10
True or False Questions:
- cos 2A = cos² A – sin² A is True.
- tan 2A = (2 tan A)/(1+tan²A) is False.
- cos 2A = 2 cos² A + 1 is False.
- cos 2A = 1 + 2 sin² A is False.
- sin(-x) = sin x is False.
- Cosine and its reciprocal are even functions is True.
- tan(-x) = tan(x) is False.
- Cot (-x) = cot x is False.
- Sine and its reciprocal are odd functions is True.
- Sin (A + B) = sin A cos B + cos A sin B is True.
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