56.5k views
3 votes
Why is sin(20) = sin(160) = -sin(200) = -sin(340)?

User Joe Pigott
by
8.2k points

2 Answers

2 votes
Because they're all the same distance from the x axis on a coordinate plane. Also, remember that in quadrant I, all trig values are positive. In Q II, only sine and cosecant are positive. In Q III, only tangent and cotangent are positive. In Q IV, only cosine and secant are positive. Think of it as All Students Take Calculus.
User Vikum Dheemantha
by
7.2k points
5 votes

Answer:

see.

Explanation:

The value of sin is the same at the same distance from the cuadrant limit of the point. For the case of 20°, we have that the sin is the same in the following case:

As 20 is positive we use the limit cuadrant at 90°. The distance of 20 to 90 is 70. So, sin(20)=sin(90+70)=sin(160).

Also we have that sin(x) is a odd function, so sin(-x)=-sin(x), so

sin(-20°)= -sin(20°)

-sin(-20°)=sin(20°)

-sin(340°)=sin(20°).

and,

sin(-160°)=-sin(160°)

-sin(-160°)=sin(160°)

-sin(200°)=sin(160°)=sin(20°).

User Bilal Rabbani
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories