Semester Pre-Cal Review

Front

What is the equation for the angle in standard position that corresponds to the angle \(\theta = -\frac{5\pi}{4}\)?

Back

The angle \(\theta = -\frac{5\pi}{4}\) is in the third quadrant and can be expressed in standard position as \(\theta = \frac{3\pi}{4}\) or \(\theta = \frac{7\pi}{4}\) when converted to a positive angle.

Front

What is a reference angle?

Back

A reference angle is the acute angle formed by the terminal side of an angle in standard position and the x-axis. It is always positive and less than or equal to 90°.

Front

What is the reference angle for 125°?

Back

The reference angle for 125° is 55°.

Front

How do you find the magnitude of a vector \(\mathbf{v} = \langle a, b \rangle\)?

Back

The magnitude of a vector \(\mathbf{v} = \langle a, b \rangle\) is calculated using the formula \(||\mathbf{v}|| = \sqrt{a^2 + b^2}\).

Front

What is the magnitude of the vector \(\langle -4, -6 \rangle\)?

Back

The magnitude of the vector \(\langle -4, -6 \rangle\) is approximately 7.211.

Front

What is the sine function in relation to a right triangle?

Back

In a right triangle, the sine of an angle \(\theta\) is defined as the ratio of the length of the opposite side to the length of the hypotenuse: \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\).

Front

What is the value of \(\sin(\theta)\) if the opposite side is 4 and the hypotenuse is 5?

Back

The value of \(\sin(\theta)\) is \(\frac{4}{5}\).

Front

What is the cosine function in relation to a right triangle?

Back

In a right triangle, the cosine of an angle \(\theta\) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse: \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\).

Front

What is the value of \(\cos(\theta)\) if the adjacent side is 3 and the hypotenuse is 5?

Back

The value of \(\cos(\theta)\) is \(\frac{3}{5}\).

Front

What is the tangent function in relation to a right triangle?

Back

In a right triangle, the tangent of an angle \(\theta\) is defined as the ratio of the length of the opposite side to the length of the adjacent side: \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\).