Problem 15
Question
Convert each angle in degrees to radians. Express your answer as a multiple of \(\pi\). $$135^{\circ}$$
Step-by-Step Solution
Verified Answer
The angle \(135^{\circ}\) is equal to \(\frac{3\pi}{4}\) radians when expressed as a multiple of \(\pi\).
1Step 1: Understand the Conversion Formula
Firstly, it must be remembered that the relationship between degrees and radians is provided by the formula \(1^{\circ} = \frac{\pi}{180} \) radians. This is how we can interconvert these two units of angle measure.
2Step 2: Apply the Conversion Formula
Next, multiply the given angle in degrees by the conversion factor. This is done by multiplying \(135^{\circ}\) by \(\frac{\pi}{180}\) to get the radian measure.
3Step 3: Simplify the Expression
Simplify the resulting fraction as follows: \(\frac{(135\pi)}{180} = \frac{3\pi}{4}\).
Other exercises in this chapter
Problem 14
In Exercises \(9-16\), evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. $$\cos \frac{3 \pi}{2}$$
View solution Problem 15
Determine the amplitude and period of each function. Then graph one period of the function. $$y=-\sin \frac{2}{3} x$$
View solution Problem 15
Find the exact value of each expression. $$\tan ^{-1} 0$$
View solution Problem 15
In Exercises \(9-16\), evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. $$\cot \frac{\pi}{2}$$
View solution