Trigonometry Test

Front

What is the formula for secant in terms of cosine?

Back

Secant is defined as the reciprocal of cosine: \( \sec x = \frac{1}{\cos x} \).

Front

What is the value of \( \sin 30^{\circ} \)?

Back

The value of \( \sin 30^{\circ} \) is \( \frac{1}{2} \).

Front

What is the value of \( \cos 60^{\circ} \)?

Back

The value of \( \cos 60^{\circ} \) is \( \frac{1}{2} \).

Front

What are the three main trigonometric ratios?

Back

The three main trigonometric ratios are sine, cosine, and tangent.

Front

How do you simplify \( \sec 2x (1 - \sin 2x) \)?

Back

The expression simplifies to 1.

Front

What is the relationship between sine and cosine in a right triangle?

Back

In a right triangle, \( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} \) and \( \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} \).

Front

What is the tangent ratio in terms of sine and cosine?

Back

The tangent ratio is defined as \( \tan \theta = \frac{\sin \theta}{\cos \theta} \).

Front

What is the Pythagorean identity involving sine and cosine?

Back

The Pythagorean identity states that \( \sin^2 x + \cos^2 x = 1 \).

Front

How do you calculate the sine of an angle using a unit circle?

Back

In the unit circle, the sine of an angle is the y-coordinate of the point where the terminal side of the angle intersects the circle.

Front

What is the value of \( 5\sin 30^{\circ} - 3\cos 60^{\circ} \)?

Back

The value is 1.