Trigonometry Final Exam Review Fall '24

Front

What is the Pythagorean identity in trigonometry?

Back

The Pythagorean identity states that for any angle \( \theta \), \( \sin^2(\theta) + \cos^2(\theta) = 1 \).

Front

Define sine, cosine, and tangent in terms of a right triangle.

Back

Sine (sin) is the ratio of the opposite side to the hypotenuse. Cosine (cos) is the ratio of the adjacent side to the hypotenuse. Tangent (tan) is the ratio of the opposite side to the adjacent side.

Front

What is the value of \( \sin(90^\circ) \)?

Back

The value of \( \sin(90^\circ) \) is 1.

Front

What is the value of \( \cos(180^\circ) \)?

Back

The value of \( \cos(180^\circ) \) is -1.

Front

What is the relationship between sine and cosecant?

Back

Cosecant (csc) is the reciprocal of sine: \( \csc(\theta) = \frac{1}{\sin(\theta)} \).

Front

If \( \sin(\theta) = \frac{15}{17} \) and \( \cos(\theta) < 0 \), what is \( \tan(\theta) \)?

Back

\( \tan(\theta) = -\frac{15}{8} \).

Front

What is the value of \( \theta \) if \( \cos(\theta) = -1 \)?

Back

\( \theta = 180^\circ \) or \( \theta = \pi \) radians.

Front

On the unit circle, what is the angle corresponding to the point \( \left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right) \)?

Back

The angle is \( \frac{5\pi}{6} \) radians.

Front

What is the cotangent of \( 480^\circ \)?

Back

The cotangent of \( 480^\circ \) is \( -\frac{\sqrt{3}}{3} \).

Front

What is the formula for converting degrees to radians?

Back

To convert degrees to radians, use the formula: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \).