Topic 8 - Trigonometric Equations and Identities

Which of these is necessary to define the inverse cosine function?

• The cosine function must be always increasing.

• The range of the cosine function must be y | y ≥ 0 .

• The domain of the cosine function must be restricted to 0 ≤ x ≤ π .

• The cosine function must be periodic.

• −45°

• −60°

Solve 3 sin θ + 2 = sin θ + 1 for values between 0 and 2π .

The average daily high temperature in Seattle is modeled by the function T = −15 cos ( πm/6 ) + 61 , where T is the temperature in °F, and m is the number of months since the beginning of the year. What is the value of m when the average daily high temperature T is 76°F? (Hint: Isolate the trig function and see what value of m gives you that correct y value.

Mathematical Equivalence

ON

In △LMN , m∠L = 108° , m∠M = 25° , and 𝓁 = 12 . What is m ?

• about 0.19

• about 5.3

• about 20.8

• 27

Tia uses the Law of Cosines to find a missing length in △ABC . After Tia substitutes the values she knows into the equation and simplifies, she gets −23.26 cos A = 0 . What does this tell you about △ABC ?

• There are two possible triangles that match the information Tia is using.

• The triangle is a right triangle.

• There is no triangle that matches the information Tia is using.

• The triangle is an obtuse triangle.

What is the length y ? Round to the nearest tenth.

Mathematical Equivalence

ON

A path in a park forms a triangle as shown. What is the measure of angle A? Round to the nearest tenth of a degree.

Mathematical Equivalence

ON

What is the correct identity/relationship? cos (−θ) = ?

• cos θ

• − cos θ

A simplified form of the expression 1 − (cot² x)(sin² x) is (a)