Question

if theta is an acute angle and 3 cos square theta is equal to 9/4 then find the value of theta​

Answer 1

Answer:

Required value of theta is 30°.

Step-by-step explanation:

Given,and 3 cos square theta is equal to 9/4

We can write it

$3{cos}^{2} \theta = \frac{9}{4} \\ {cos}^{2} \theta = \frac{3}{4} cos \theta = \sqrt{ \frac{3}{4} } \\ cos \theta = \frac{ \sqrt{3} }{2} \\ cos \theta = \cos( {30}^{o} ) \\ \theta = {30}^{o}$

Here applied formula,

$cos {30}^{o} = \frac{ \sqrt{3} }{2}$

and

$if \: \cos(x) = \cos(y) then \: x = y$

This is a problem of Trigonometry.

Some important Trigonometry related information,

Trigonometry is the branch of mathematics that studies the relationships between the side lengths and angles of triangles. The field emerged in the Hellenistic world in the 3rd century BC, from applications of geometry to astronomical studies. The Greeks focused on calculating chords, while Indian mathematicians created the earliest known tables of values for trigonometric ratios (also called trigonometric functions). like sinus.

Throughout history, trigonometry has been applied to fields such as geodesy, surveying, celestial mechanics, and navigation.

Trigonometry is known for its many identities. These trigonometric identities are commonly used to rewrite trigonometric expressions with the goal of simplifying the expression, finding a more useful form for the expression, or solving an equation.

know more about Trigonometry,

https://brainly.in/question/8632966

https://brainly.in/question/11371684

#SPJ1