Angles and Trigonometric Functions Answers

Which trigonometric expressions equal ? Check all that apply.

Multiplying both sides of the above equations by r, we get that x = r cos(θ) and y = r sin(θ).

definition of cosine✔ definition of sinePythagorean theorem

definition of cosinedefinition of sine✔ Pythagorean theorem

multiplicationsimplification✔ substitution

associative propertydistributive property✔ laws of exponents

Which trigonometric values equal 0? Check all that apply.sin(3π)cos(–360°)tan(900°)cot(0°)

Given and , use trigonometric identities to find the the value of cot(30°).

Given , what is cos(t)?

A bicycle wheel with diameter 16 inches rides over a screw in the street. The screw is on level ground before it punctures the bike’s tire. After the bike has moved forward another 56π inches, how high above the ground is the screw? Round to the nearest tenth of an inch.

A water wheel has a radius of 4 feet and the bottom of the wheel is 1 foot from the ground. One plank is painted white and it starts at the top of the wheel. The wheel is rolled forward through an angle of radians. How high from the ground is the white plank after this motion?

A regular hexagon inscribed in a circle creates 6 equiangular triangles. If the radius of the circle is 10 inches, how far are points at A and B from the y-axis?

By , cos(θ) = , and by , sin(θ) = . Multiplying both sides of the above equations by r, we get that x = r cos(θ) and y = r sin(θ). The states that x2 + y2 = r2. By , we have[r cos(θ)]2 + [r sin(θ)]2 = r2. Applying the , the equation can be written as r2 cos2(θ) + r2 sin2(θ) = r2. Dividing both sides of the equation by r2 results in cos2(θ) + sin2(θ) = 1.