Trig - Unit Circle Test - Review

Front

What is the range of the angle \( \theta \) when solving trigonometric equations in the unit circle?

Back

The range of the angle \( \theta \) is \( 0 \leq \theta < 2\pi \).

Front

How do you solve the equation \( -1 + 3\sin\theta = -4 \)?

Back

Add 1 to both sides to get \( 3\sin\theta = -3 \), then divide by 3 to find \( \sin\theta = -1 \). The solution is \( \theta = \frac{3\pi}{2} \).

Front

What are the solutions for the equation \( 2 + 2\cos\theta = 1 \)?

Back

Subtract 2 from both sides to get \( 2\cos\theta = -1 \), then divide by 2 to find \( \cos\theta = -\frac{1}{2} \). The solutions are \( \theta = \frac{2\pi}{3}, \frac{4\pi}{3} \).

Front

How do you convert radians to degrees?

Back

To convert radians to degrees, multiply the radian measure by \( \frac{180}{\pi} \).

Front

What is the degree measure of \( \frac{4\pi}{3} \)?

Back

The degree measure of \( \frac{4\pi}{3} \) is 240˚.

Front

What is the degree measure of \( \frac{5\pi}{9} \)?

Back

The degree measure of \( \frac{5\pi}{9} \) is 100˚.

Front

What is the formula for arc length in a circle?

Back

The formula for arc length \( s \) is \( s = r\theta \), where \( r \) is the radius and \( \theta \) is the central angle in radians.

Front

How do you find the arc length for a radius of 20 and a central angle of 138˚?

Back

First, convert 138˚ to radians: \( \theta = \frac{138\pi}{180} = \frac{23\pi}{30} \). Then use the formula: \( s = 20 \cdot \frac{23\pi}{30} = \frac{46\pi}{3} \).

Front

What is the sine of an angle in the unit circle?

Back

The sine of an angle \( \theta \) is the y-coordinate of the point on the unit circle corresponding to that angle.

Front

What is the cosine of an angle in the unit circle?

Back

The cosine of an angle \( \theta \) is the x-coordinate of the point on the unit circle corresponding to that angle.