If sinΘ

_{1}+ sinΘ_{2}+ sinΘ_{3}= 3 then cosΘ_{1}+ cosΘ_{2}+ cosΘ_{3 }=?If sinΘ_{1} + sinΘ_{2} + sinΘ_{3} = 3 then cosΘ_{1} + cosΘ_{2} + cosΘ_{3 }=?

Tutors, please sign in to answer this question.

Bridgewater, NJ

As mentioned, the maximum value of the sine function is 1. Thus, the only way the sum of the sines of 3 distinct angles can be 3 is if each sine is equal to 1. The only angles for which sine is 1 (in radians) are ∏/2+2N∏, where N covers all natural numbers (note I am using capital pi here to represent 3.1415... or 180 deg... b/c lowercase pi looked like an "n")...in other words 90 degrees or any other
*version*, so to say, of 90 degrees (i.e. any multiple of 360 degrees added to 90 deg) has its sine as 1.

By the Pythagorean identity, the sum of the squares of sine and cosine of the same angle is always 1. Hence, if sine of an angle is already 1, what must the cosine of that angle be?

This should answer the question...

Reston, VA

The maximum the sine can be is 1. Therefore, each theta has to be either at 0, pi, 2pi, etc. (0, 18, 360, ...)

You should look at a picture of the sine graph and the cosine graph. The cosine is the same shape as the sine but off by 90 degrees or pi/2. When the sine is 1, the cosine is 0. You can also see this on your unit circle diagram which you should review. Therefore you can see what the sum of the cosines of those angles will be.

Dorene O.

Daisy C.

Effective ELA Tutor - Boston College Graduate - Masters Degree ELA/ESL

Atlantic Beach, NY

5.0
(134 ratings)

Jeffrey G.

Former Med-Student turned Professional Science Tutor

Brooklyn, NY

5.0
(371 ratings)

Jennifer C.

Experienced Educator Specializing in Test Prep and Enrichment

Brooklyn, NY

5.0
(74 ratings)

- Math Help 5208
- Algebra 4923
- Math Word Problem 4260
- Calculus 2164
- Word Problem 4959
- Algebra 2 3299
- Algebra 1 3947
- Math Problem 974
- Math Help For College 1361
- Math Equations 938