Q: Which trigonometric identity is correct?

$$\sin^2$(\theta) + \cos^2$(\theta) = 1$$

Question 1

Given a unit circle centered at the origin, what is the value of $$\sin(45^\circ)$$?

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 2

If a point $$P on $$the unit circle has coordinates $$(x, y)$$ and corresponds to an angle $$	heta$$ measured from the positive $$x-$$axis, which equation correctly relates $$y to$$ $$	heta$$?

Accepted Answer

$$y = \sin(	heta)$$

Question 3

A square is inscribed in a unit circle. What is the length of the diagonal of the square?

Accepted Answer

$$\sqrt{2}$$

Question 4

Which of the following is the correct value for $$\cos(30^\circ)$$?

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 5

If $$	an(	heta) = 1$$, what is the value of $$	heta in $$degrees between $$0^\circ$$ and $$90^\circ$$?

Accepted Answer

$$45^\circ$$

Question 6

A right triangle has legs of length $$1$$ and $$\sqrt{3}. $$What is the measure of the angle opposite the leg of length $$1$$?

Accepted Answer

$$30^\circ$$

Question 7

Which trigonometric function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle?

Accepted Answer

$$\cos(	heta)$$

Question 8

If $$\sin(	heta) = \frac{1}{2}$$ and $$0^\circ \u003c 	heta \u003c 90^\circ$$, what is $$	heta$$?

Accepted Answer

$$30^\circ$$

Question 9

What is the value of $$	an(60^\circ)$$?

Accepted Answer

$$\sqrt{3}$$

Question 10

A ladder leans against a wall making a $$60^\circ$$ angle with the ground. If the ladder is $$10$$ meters long, how high up the wall does it reach?

Accepted Answer

$$10 	imes \sin(60^\circ)$$

Question 11

Which of the following is the correct value for $$\sin(90^\circ)$$?

Accepted Answer

$$1$$

Question 12

If $$\cos(	heta) = 0$$, what is a possible value for $$	heta$$ between $$0^\circ$$ and $$360^\circ$$?

Accepted Answer

$$90^\circ$$

Question 13

A square is inscribed in a circle of radius $$r. $$What is the length of a side of the square?

Accepted Answer

$$r\sqrt{2}/2$$

Question 14

Which trigonometric identity is correct?

Accepted Answer

$$\sin^2$(	heta) + \cos^2$(	heta) = 1$$

Question 15

If $$\sin(	heta) = \cos(	heta)$$ and $$0^\circ \u003c 	heta \u003c 90^\circ$$, what is $$	heta$$?

Accepted Answer

$$45^\circ$$

Study Notes: Graphs, Functions, and Models in Trigonometry

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