SOLUTION: Given that Sin theta = -3/5 , 3pi/2 , theta , 2pi, Find: Sin20 Cos20 Tan20

Algebra ->  Trigonometry-basics -> SOLUTION: Given that Sin theta = -3/5 , 3pi/2 , theta , 2pi, Find: Sin20 Cos20 Tan20      Log On


   

Question 1075182: Given that Sin theta = -3/5 , 3pi/2 , theta , 2pi,
Find:
Sin20
Cos20
Tan20
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given that Sin theta = -3/5 , 3pi/2 <= theta < 2pi,
Find:
Sin20
Cos20
Tan20
~~~~~~~~~~~~~~~~~~ 

0.  cos%28theta%29 = sqrt%281-sin%5E2%28theta%29%29 = sqrt%281-%28-3%2F5%29%5E2%29 = sqrt%281-9%2F25%29 = sqrt%2816%2F25%29 = 4%2F5.

    The sign is "+", since cosine is positive in QIV.


1.  sin%282theta%29 = 2%2Asin%28theta%29%2Acos%28theta%29 = 2%2A%28-3%2F5%29%2A%284%2F5%29 = -24%2F25.


2.  cos%282theta%29 = 1-2%2Asin%5E2%28theta%29 = 1-2%2A%28-3%2F5%29%5E2 = 1+-+2%2A%289%2F25%29 = 7%2F25.


        ( In particular, 2theta%29 lies in QIV ).


3.  Having this, can you calculate tan%282theta%29%29 on your own ?


For many other similar solved problems see the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Trigonometry: Solved problems".