Question

find the value of sin 1380°​

Answer 1

Step-by-step explanation:

1380-3*360=1380-1080=300

sin(1380)=sin(300)=sin(60)=-√3/2 (in Q4 where sin<0)

..

cos(225)=cos(45)=-√2/2 (in Q3 where cos<0)

..

420-360=60

tan(420)=tan(60)=√3 (in Q1 where tan>0)

Answer 2

The value of $\mathsf{sin1380^{o}}$ is $\mathsf{(-\dfrac{\sqrt{3}}{2})}$.

Concept to be used:

First of all we must have some trigonometric ideas that would help us solve the problem:

• In the first and the second quadrant, sin is always positive. In other quadrants, it is negative.

• In the first and the third quadrant, tan is always positive. In other quadrants, it is negative.

• In the first and the fourth quadrant, cos is always positive. In other quadrants, it is negative.

Step-by-step explanation:

Now, $\mathsf{sin1380^{o}}$

$\mathsf{=sin(15\times 90^{o}+30^{o})}$

• [ It lies in the fourth quadrant and in fourth quadrant the symbol of $\mathsf{sin}$ is negative and being an odd multiple of $\mathsf{90^{o}}$, it changes into $\mathsf{cos}$. ]

$\mathsf{=-cos30^{o}}$

$\mathsf{=-\dfrac{\sqrt{3}}{2}}$

#SPJ3