12 Questions
What is the reciprocal of the trigonometric identity tangent?
Cotangent = 1/tangent
If sine x = 5/7 in quadrant two, what is the value of cosine x?
2√6/7
What is cosecant x if tangent x = -8/15 in quadrant four?
-17/8
Where does sine negative x equal -sin x?
Quadrant four
What is the equivalent of cosine negative 150 using cofunction identity and quadrant properties?
-cosine 210
How can coterminal angles be determined?
By adding or subtracting multiples of 360 degrees
What is the simplified form of the expression 1 + sin^2(40) + sin^2(50)?
cos^2(40)
According to the Pythagorean identity, what is the relationship between sine squared and cosine squared of an angle?
Their product is equal to one
In a 30-60-90 reference triangle, what is the exact value of cosine 60?
1/2
How can the exact value of cosine 210 be found without a calculator?
Using the reference angle of 30 degrees
What is the exact value of tangent 30 using the unit circle?
-√3/3
How is the reference angle of an angle in quadrant four calculated?
Subtracting the angle from 360 degrees
Study Notes
- The video focuses on solving basic trigonometry problems by converting degrees to radians using the formula degrees * pi / 180 to cancel out the degree symbol.
- Negative angles are measured clockwise, and positive angles are measured counterclockwise.
- Coterminal angles land in the same position on the graph and can be found by adding or subtracting multiples of 360 degrees.
- To find the arc length, use the formula arc length = angle in radians * radius, after converting the angle from degrees to radians.
- For finding the value of sine x in a right triangle, use the SOHCAHTOA rule where sine = opposite/hypotenuse.
- Reciprocal trigonometric identities include secant = 1/cosine and cotangent = 1/tangent.
- To find the value of secant x, first find the value of cosine using the adjacent side and hypotenuse ratio, then calculate secant as 1/cosine.- Sine x = 7/25, in quadrant one, creates a 7-24-25 triangle, allowing to find tangent x as 7/24.
- In quadrant four, with tangent x = -8/15, the missing side in the triangle is 17, leading to cosecant x = -17/8.
- For sine x = 5/7 in quadrant two, cosine x is found by applying the Pythagorean identity to get 2√6/7.
- The quadrant in which sine z < 0 and cosine z > 0 is quadrant four.
- Sine negative x = -sin x, cosine negative x = cos x, and cotangent negative x = -cotan x.
- Sine pi/5 is equivalent to cosine 3pi/10.
- Cosine negative 150 is equivalent to cosine 210, found by applying cofunction identity and quadrant properties.
- The expression 1 + sin^2(40) + sin^2(50) can be simplified by recognizing that sin 50 = cos 40, leading to cos^2(40).
- The Pythagorean identity for sine and cosine states that sine squared plus cosine squared equals one.
- To find the exact value of cosine 60 without a calculator, you can use the 30-60-90 reference triangle where cosine 60 is equal to 1/2.
- Another method to find trigonometric values without a calculator is by using the unit circle, where cosine 60 is also equal to 1/2.
- To find the exact value of sine pi over 4, first convert the angle to degrees (45 degrees) and then use the 45-45-90 reference triangle to determine that sine 45 is equal to the square root of 2 divided by 2.
- The exact value of tangent 30 can be found using the 30-60-90 triangle, where tangent 30 is equal to the square root of 3 divided by 3.
- Using the unit circle, tangent 30 can also be found by dividing the y-coordinate by the x-coordinate, resulting in the same value: square root of 3 divided by 3.
- The reference angle of 290 degrees can be calculated by subtracting the angle from 360 since it lies in quadrant four, resulting in a reference angle of 70 degrees.
- In finding the exact value of cosine 210 without a calculator, first determine that 210 degrees is in quadrant three and calculate the reference angle as 30 degrees.
- Using the 30-60-90 reference triangle, cosine 210 can be evaluated as negative square root of 3 divided by 2.
Explore basic trigonometry concepts including converting degrees to radians, coterminal angles, arc length, reciprocal trigonometric identities, and finding exact values without a calculator using reference triangles and the unit circle.
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