Grade 11 Math: Area & Cosine Rule Quiz & Flashcards

What is the formula for the area of a triangle using the Area Rule?

$\frac{1}{2} bc \sin A$

When should you use the Sine Rule?

When you know two sides and a non-included angle.

What is the formula for the Cosine Rule?

$a^2 = b^2 + c^2 - 2bc \cos A$

In which quadrant is the tangent function positive?

Quadrant III Signup and view all the answers

What is the condition for using the Cosine Rule?

Two sides and the included angle are given. Signup and view all the answers

When can you use the Area Rule?

When no perpendicular height is given. Signup and view all the answers

What is the purpose of the CAST diagram?

To remember the signs of trigonometric functions in different quadrants. Signup and view all the answers

What is a general solution of a trigonometric equation?

A solution that takes into account the periodic nature of the trigonometric functions. Signup and view all the answers

What is the main difference between the Sine Rule and the Cosine Rule?

The Sine Rule is used for solving triangles with two sides and a non-included angle, while the Cosine Rule is used for solving triangles with two sides and the included angle. Signup and view all the answers

If you are given two sides and the included angle of a triangle, which rule should you use to solve the triangle?

The Cosine Rule Signup and view all the answers

In which quadrant is the cosine function positive?

Quadrant IV Signup and view all the answers

What is the purpose of the CAST diagram in trigonometry?

To represent the signs of trigonometric functions in different quadrants Signup and view all the answers

If you are given two angles and a side of a triangle, which rule should you use to solve the triangle?

The Sine Rule Signup and view all the answers

What is the main difference between the Area Rule and the other two trigonometric rules?

The Area Rule is used for finding the area of a triangle, while the other two rules are used for finding the lengths of sides and the measures of angles. Signup and view all the answers

If you are given three sides of a triangle, which rule should you use to solve the triangle?

The Cosine Rule Signup and view all the answers

What is the characteristic of a general solution to a trigonometric equation?

It takes into account the periodic nature of the trigonometric functions Signup and view all the answers

What is the condition for using the Area Rule?

When no perpendicular height is given Signup and view all the answers

In which quadrants are the sine and cosine functions positive?

Quadrant I and Quadrant IV Signup and view all the answers

What is the characteristic of the Sine Rule?

It is used when no right angle is given Signup and view all the answers

What is the purpose of the CAST diagram?

To identify the trigonometric functions that are positive in each quadrant Signup and view all the answers

When can you use the Cosine Rule?

When three sides are given Signup and view all the answers

What is the main difference between the Area Rule and the other two trigonometric rules?

It is used to find the area of a triangle Signup and view all the answers

What is the condition for using the Sine Rule?

When two angles and a side are given Signup and view all the answers

What is the formula for the area of a triangle using the Area Rule, when two sides and the included angle are given?

All of the above Signup and view all the answers

If a triangle has two sides of length 5 and 7, and the angle between them is 60°, which rule would be used to find the length of the third side?

Cosine Rule Signup and view all the answers

In which quadrant is the value of sin(x) equal to the value of cos(x)?

Quadrant II Signup and view all the answers

What is the general solution to the equation sin(x) = 1/2?

x = 30° + 360°k Signup and view all the answers

If a triangle has two angles of 30° and 60°, and one side of length 5, which rule would be used to find the length of the other two sides?

Sine Rule Signup and view all the answers

What is the value of cos(A) in a triangle with sides of length 3, 4, and 5, and angle A opposite the side of length 4?

3/5 Signup and view all the answers

In which quadrant(s) is the value of tan(x) negative?

Quadrant II and IV Signup and view all the answers

What is the value of sin(B) in a triangle with sides of length 5, 7, and 8, and angle B opposite the side of length 7?

7/8 Signup and view all the answers

If a triangle has three sides of length 5, 7, and 8, which rule would be used to find one of its angles?

Cosine Rule Signup and view all the answers

Gr 11 Math Ch 6: Area, Sine and Cosine Rules

Questions and Answers

What is the formula for the area of a triangle using the Area Rule?

When should you use the Sine Rule?

What is the formula for the Cosine Rule?

In which quadrant is the tangent function positive?

What is the condition for using the Cosine Rule?

When can you use the Area Rule?

What is the purpose of the CAST diagram?

What is a general solution of a trigonometric equation?

What is the main difference between the Sine Rule and the Cosine Rule?

If you are given two sides and the included angle of a triangle, which rule should you use to solve the triangle?

In which quadrant is the cosine function positive?

What is the purpose of the CAST diagram in trigonometry?

If you are given two angles and a side of a triangle, which rule should you use to solve the triangle?

What is the main difference between the Area Rule and the other two trigonometric rules?

If you are given three sides of a triangle, which rule should you use to solve the triangle?

What is the characteristic of a general solution to a trigonometric equation?

What is the condition for using the Area Rule?

In which quadrants are the sine and cosine functions positive?

What is the characteristic of the Sine Rule?

What is the purpose of the CAST diagram?

When can you use the Cosine Rule?

What is the main difference between the Area Rule and the other two trigonometric rules?

What is the condition for using the Sine Rule?

What is the formula for the area of a triangle using the Area Rule, when two sides and the included angle are given?

If a triangle has two sides of length 5 and 7, and the angle between them is 60°, which rule would be used to find the length of the third side?

In which quadrant is the value of sin(x) equal to the value of cos(x)?

What is the general solution to the equation sin(x) = 1/2?

If a triangle has two angles of 30° and 60°, and one side of length 5, which rule would be used to find the length of the other two sides?

What is the value of cos(A) in a triangle with sides of length 3, 4, and 5, and angle A opposite the side of length 4?

In which quadrant(s) is the value of tan(x) negative?

What is the value of sin(B) in a triangle with sides of length 5, 7, and 8, and angle B opposite the side of length 7?

If a triangle has three sides of length 5, 7, and 8, which rule would be used to find one of its angles?

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