How do you find the sine or cosign on an angle without a calculator?

Mathematics
Tutor: None Selected Time limit: 1 Day

In my class we are not allowed to use calculators on math tests. So I was hoping to find a way to calculate the sin or cos of an angle without using a calculator.  I would also prefer not to use memorize a unit circle.  I've learned the rules for the special triangles but how do I figure out problems like sin(15) or cos(65) etc.? 

Oct 3rd, 2015

Thank you for the opportunity to help you with your question!

Use the special angles. These are 0, 30, 45, 60, 90

and use the angle difference identities like Sin(A-B) = Sin A cos B - Cos A Sin B
There are more formulas for Sin (A+B), cos (A+B), etc you must have been taught these.

.
sin 15 = sin (45-30) = sin 45 cos 30 - sin 30 cos 45
simplify these angles ((sqrt 2)/2 * (sqrt 3)/2 - 1/2 *(sqrt 2)/2)
Simplify these and you will have your answer. Combine like terms.

Let me know incase you need any further help ! Thanks :)
Sep 19th, 2015

Did you know? You can earn $20 for every friend you invite to Studypool!
Click here to
Refer a Friend
...
Oct 3rd, 2015
...
Oct 3rd, 2015
Dec 8th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer