Question

Given sin θ = square root of 23 divided by 12 and tan θ = square root of 23 divided by 11, find cos θ. Enter the answer as a fraction in lowest terms.

Answer 1

Answer:

11/12

Step-by-step explanation:

tan θ = sin θ / cos θ

cos θ = sin θ / tan θ

cos θ = (√23/12) / (√23/11)

cos θ = (√23/12) × (11/√23)

cos θ = 11/12

Answer 2

Using the relationship between sine, cosine, and tangent. Then the value of $\rm cos \theta$ is $\dfrac{11}{12}$.

What is an angle?

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Given

$\rm sin \theta = \dfrac{\sqrt{23} }{12} \ \ and \ \ tan \theta = \dfrac{\sqrt{23} }{11}$

The value of $\rm cos\ \theta$ will be

We know the relationship between sine, cosine, and tangent is given.

$\rm tan \theta = \dfrac{sin \theta }{cos \theta}$

Put the value,

$\rm tan \theta = \dfrac{sin \theta }{cos \theta}\\\\\rm cos \theta = \dfrac{sin \theta }{tan \theta}\\\\cos \theta = \dfrac{\frac{\sqrt{23} }{12}}{\frac{\sqrt{23} }{11}}\\\\cos \theta = \dfrac{11}{12}$

Thus, the value of $\rm cos \theta$ is $\dfrac{11}{12}$.

More about the angle link is given below.

https://brainly.com/question/15767203