## Anikate one year ago find all solutions: sec^2 theta -sec theta -2= 0 i'll post the equation

1. Anikate

|dw:1434503139480:dw|

2. mathstudent55

This is a quadratic equation in sec theta. You can do a substitution. Replace sec theta with x. Solve the quadratic. Then replace x with sec theta in all the solutions and solve the trig part.

3. Anikate

|dw:1434503305674:dw|

4. Anikate

now substitute x for $\sec \theta$ ?

5. anonymous

in coordination with what 'mathstudent55' here is a picture.

6. mathstudent55

No. That is not what I meant. Don't just replace theta with x. Let sec(theta) = x Then sec^2(theta) = x^2 Now rewrite the original equation with x^2 instead of sec^2(theta) and with x instead of sec(theta). That's the substitution you make.

7. Anikate

oh

8. anonymous

now solve for x

9. Anikate

|dw:1434503782102:dw|

10. Anikate

ok

11. mathstudent55

|dw:1434503819026:dw|

12. Anikate

|dw:1434503813310:dw|

13. Anikate

|dw:1434503847634:dw|

14. anonymous

look at the pic i attached

15. mathstudent55

|dw:1434503868680:dw|

16. mathstudent55

Good. we have the same. Now find the two values of x.

17. mathstudent55

Can you finish the quadratic and find the values of x? |dw:1434504047082:dw|

18. Anikate

x= 2 and x=-1 @mathstudent55

19. mathstudent55

Correct. We have finished solving the quadratic equation part of this problem. Now we need to solve the trig part of this equation. We now need to substitute back what we did above. |dw:1434504555288:dw|

20. mathstudent55

Since above we let sec(theta) equal x, we replace x with what it really is, sec(theta)

21. mathstudent55

|dw:1434504659195:dw|

22. mathstudent55

Now we need to solve for theta.

23. mathstudent55

The secant is the reciprocal of what trig function?

24. mathstudent55

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25. mathstudent55

Where is the cosine function equal to 1/2, and where is the cosine function equal to -1?