## anonymous 5 years ago 2cos theta = sec theta.. what are they asking me to find?

1. anonymous

$\theta$

2. anonymous

$2\cos\theta=\sec\theta$

3. anonymous

the exact values of the degree?

4. anonymous

i would think so

5. anonymous

on what interval?

6. anonymous

0 degree to 360 degree

7. anonymous

$2\cos{\theta}=\sec{\theta} \rightarrow 2\cos{\theta}=\frac{1}{\cos{\theta}}$then$2\cos^2{\theta}=1$

8. anonymous

$\cos{\theta}={\pm}\frac{1}{\sqrt{2}}$

9. anonymous

Find all those angles theta that satisfy this.

10. anonymous

θ = 45, 215, 135, 225

11. anonymous

itsmesowat.. how'd you get the answers?

12. anonymous

use your unit circle or other favorite method to get special angle values for consine...

13. anonymous

use the calculator do [2nd] [cos] of the fraction 1/rad(2)

14. anonymous

Draw a right-angled triangle with sides 1, 1 and hypotenuse sqrt(2). cos(theta)=1/sqrt(2) when theta = 45 degrees. In the second quadrant, 180-45 = 135 degrees, in the third, 180+45 degrees = 225 and in the fourth, 360-45 = 315 degrees/

15. anonymous

gotcha.

16. anonymous

you got everything lokisan said? you are a genius!!~~~~

17. anonymous

lol tyler.. where'd you get 215 degrees?

18. anonymous

215 is typo, should be 225, which is 180+45, reference angle of 135

19. anonymous

gotcha.

20. anonymous

sorry i suck at typing out math... they should introduce the white board on this haha

21. anonymous

lmao. XD

22. anonymous

they have these equation thingys. it's built from mathjax

23. anonymous

wait. how'd you get 1/sqrt of 2?

24. anonymous

2cos^2(theta)=1. Divide both sides by 2, then take the sqrt of both sides.