Trig. Questions using square root and degrees

Question

What is the exact value of Sin 5Π/3

What is the exact value of Sin 11Π/6

What is the exact value of Sin 45^o

What is the exact value of Sin 30^o

What is the exact value of Sin 90^o

Answer 1

Highly recommended for trig students:

Memorize the Quadrant I sin and cos values for the 'standard' angles of:

0 degrees (= 0 radians)

30 degrees (= π/6 radians)

45 degrees (= π/4 radians)

60 degrees (= π/3 radians)

90 degrees ( = π/2 radians)

In this question, we are asked for the exact values for:

sin(5π/3) = sin(-π/3) = -sin(π/3) = - sqrt(3) / 2

sin(11π/6) = sin(-π/6) = -sin(π/6) = -1 / 2

sin(45 deg) = sqrt(2) / 2

sin 90 deg) = 1

Answer 2

Answer 3

Draw a picture using the "unit circle".

When doing this, we use 1 for the value of the hypotenuse, and then the pythagorean theorem and other tools as needed.

Example: sin (45) = √2. / 2 We can see this by drawing the 45 degree angle and recognizing that there are 2 equal "short sides" with the hypotenuse of 1. Thus, using the Pythagorean theorem, each side must be √(1/2) = 1/√2 = √2 / 2

For more, read this article:

https://www.mathsisfun.com/geometry/unit-circle.html