Question

f(theta)= sin theta and g(theta) = cos theta find the exact value of each function below if 0=60 degrees.

Answer 1

Estimate the both 2numbers 0 and 60

Answer 2

1)  $f(\theta)=\frac{\sqrt{3} }{2}$

2)  $g(\theta)=\frac{1}{2}$

3) $f(\frac{\theta}{2}) = \frac{1}{2}$

4) $g(\frac{\theta}{2} ) = \frac{\sqrt{3} }{2}$

5) $[f(\theta)]^2 =\frac{3}{4}$

6) $[g(\theta)]^2=\frac{1}{4}$

7) $f(2\theta) =\frac{\sqrt{3}}{2}$

8) $g(2\theta) =- \frac{1}{2}$

9)  $2f (\theta ) = \sqrt{3}$

10 ) $2g(\theta) = 1$

11) $f(-\theta) = -\frac{\sqrt{3} }{2}$

12) $g(-\theta) = \frac{1}{2}$

What is Trigonometry?

It is the type of mathematics that deals with the relationship between the sides and angles of triangles

1) To find $f(\theta)$

$f(\theta) \\= sin(\theta) \\= sin(60)\\ = \frac{\sqrt{3} }{2}$

2) To find $g(\theta)$

$g(\theta) \\= cos(\theta) \\= cos (60 ) \\= \frac{1}{2}$

3) To find $f(\frac{\theta}{2} )$

$f(\frac{\theta}{2}) \\\\= sin(\frac{\theta}{2}) \\\\= sin (\frac{60}{2}) \\\\= sin (30) \\\\= \frac{1}{2}$

4) To find $g(\frac{\theta}{2})$

$g(\frac{\theta}{2}) \\= cos(\frac{\theta}{2}) \\\\= cos (\frac{60}{2}) \\\\= cos(30) \\\\= \frac{\sqrt{3} }{2}$

5) To find $[f(\theta)]^2$

$[f(\theta)]^2 \\= [sin (\theta)]^2 \\= (sin(60))^2 \\= (\frac{\sqrt{3} }{2} )^2 \\= \frac{3}{4}$

6) To find $[g(\theta)]^2$

 $[g(\theta)]^2 \\= (cos( \theta))^2 \\= (cos (60 ))^2 \\= (\frac{1}{2} )^2 \\= \frac{1}{4}$

7) To find $f(2\theta)$

$f(2\theta) \\= sin(2\theta) \\= 2\times sin (\theta)\times cos (\theta) \\= 2\times sin (60)\times cos(60 )\\=2\times \frac{\sqrt{3} }{2} \times \frac{1}{2}\\ =\frac{\sqrt{3} }{2}$

8) To find $g(2\theta)$

$g(2\theta) \\= cos( 2\theta) \\= cos^2 \theta - sin^2 \theta \\=cos ^2 (60) - sin ^2 (60) \\=(\frac{1}{2} )^2 - (\frac{\sqrt{3} }{2} )^2 \\=\frac{1}{4} - \frac{3}{4} \\= -\frac{1}{2}$

9) To find $2[f(\theta)]$

$2[f(\theta)]\\=2sin(\theta)\\=2\times sin(60)\\=2\times \frac{\sqrt{3} }{2}\\ =\sqrt{3}$

10 ) To find $2[g(\theta)]$

$=2[g(\theta)]\\=2[cos(\theta)]\\=2\times [cos(60)]\\=2\times \frac{1}{2} \\=1$

11) To find $f(-\theta)$

$f(-\theta) \\= sin(- 60) \\= - sin( 60)\\= - \frac{\sqrt{3} }{2}$

12) To find $g(-\theta)$

$g(-\theta) \\=cos(-\theta)\\=cos(\theta)\\=cos(60)\\=\frac{1}{2}$

Learn more about Trigonometry:

https://brainly.com/question/12068045?referrer=searchResults

#SPJ2