QuestionFind $\alpha$ in $[0^{\circ}, 90^{\circ}]$ such that $\sec \alpha = 1.1556371$ .

Studdy Solution

STEP 1

Assumptions1. The value of $\alpha$ is in the interval $[0^{\circ},90^{\circ}]$ . $\sec \alpha=1.1556371$

STEP 2

The secant of an angle is defined as the reciprocal of the cosine of the angle. So, we can rewrite the given equation as follows $\cos \alpha = \frac{1}{\sec \alpha}$

STEP 3

Substitute the given value of $\sec \alpha$ into the equation.
$\cos \alpha = \frac{1}{1.1556371}$

STEP 4

Calculate the value of $\cos \alpha$ .
$\cos \alpha =0.865$

STEP 5

Now, we need to find the angle $\alpha$ whose cosine is $0.865$ . We can do this using the inverse cosine function, also known as arccosine.
$\alpha = \arccos(0.865)$

STEP 6

Calculate the value of $\alpha$ . Note that the result will be in radians, so we need to convert it to degrees.
$\alpha = \arccos(0.865) \times \frac{180}{\pi}$

STEP 7

Calculate the value of $\alpha$ .
$\alpha =31.1^{\circ}$ The value of $\alpha$ that satisfies the given statement is $31.1^{\circ}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms