Trig functions 5. order to find the trigonometric values for multiples of s, i,

Question

Trig functions 5. order to find the trigonometric values for multiples of s, i, and i, we use reference angles. The In initial side is on the positive I-axis. Recall angle drawn below is given in 'standard' form, i e. the z-axis that the reference angle, B, for this angle is given by the positive acute angle measured from the to the terminal side of the angle. Any trigonometric value for 0 can be found by taking the corresponding trigonometric value of B and then multiplying by t 1. To determine whether you multiply by positive 1 or negative 1, use the mneumonic, Students Take Calculus. Students All sine Take Calculus cosine tangent

Explanation / Answer

Solution:

We have to find the trigonometric values for /3, /4 and /6 in all quadrant

and we are using here reference angle here

Now take we would take 1st quadrant “ALL“ where value of all trigonometric are positive therefore we multily +1 in all trigonometric value

Let’s take = /3 ( As a reference angle )

Sin(/3) = (3/2 )* 1 = 3/2

Cos(/3) = (1/2) = 1/2

tan (/3) = 3

Cosec (/3)= 2/3

Sec (/3) = 2

Cot(/3) = 1/3

Again = /4 ( as a referance angle)

Sin(/4) = (1/2 ) = 1/2

Cos(/4) = (1/2) = 1/2

tan (/4) = 1

Cosec (/4)= 2

Sec (/4) = 2

Cot(/4) = 1

Again = /6 ( as a referance angle)

Sin(/6) = (1/2) = 1/2

Cos(/6) = (3/2)

tan (/6) = 1/3

Cosec (/6)= 2

Sec (/6) = 2/3

Cot(/6) = 3

we would take 2nd quadrant “Students“ where value of Sine and Cosine are positive therefore we multily -1 in all other trigonometric value

Let’s take = /3

Sin(/3) = (3/2 )* 1 = 3/2

Cos(/3) = (1/2) = -(1/2)

tan (/3) = -3

Cosec (/3)= 2/3

Sec (/3) = -2

Cot(/3) =-( 1/3)

Again = /4

Sin(/4) = (1/2 ) = 1/2

Cos(/4) = (1/2) = -(1/2)

tan (/4) = -1

Cosec (/4)= 2

Sec (/4) = -2

Cot(/4) = -1

Again = /6

Sin(/6) = (1/2) = 1/2

Cos(/6) = -(3/2)

tan (/6) = -(1/3)

Cosec (/6)= 2

Sec (/6) = -(2/3)

Cot(/6) = -(3)

we would take 3rd quadrant “Students“ where value of tan and Cot are positive therefore we multily -1 in all other trigonometric value

Let’s take = /3 ( As a reference angle )

Sin(/3) = (3/2 )* 1 = -(3/2)

Cos(/3) = (1/2) = -(1/2)

tan (/3) = 3

Cosec (/3)= -(2/3)

Sec (/3) = 2

Cot(/3) = -1/3

Again = /4 ( as a referance angle)

Sin(/4) = (1/2 ) = -(1/2)

Cos(/4) = (1/2) =-( 1/2)

tan (/4) = 1

Cosec (/4)= -2

Sec (/4) = -2

Cot(/4) = 1

Again = /6 ( as a referance angle)

Sin(/6) = (1/2) = -(1/2)

Cos(/6) = -(3/2)

tan (/6) = 1/3

Cosec (/6)= -2

Sec (/6) = -(2/3)

Cot(/6) = 3

we would take 4th quadrant “Students“ where value of Cos and sec are positive therefore we multily -1 in all other trigonometric value

Let’s take = /3 ( As a reference angle )

Sin(/3) = (3/2 )* 1 = -(3/2)

Cos(/3) = (1/2) = 1/2

tan (/3) = -3

Cosec (/3)= -(2/3)

Sec (/3) = 2

Cot(/3) = -(1/3)

Again = /4 ( as a referance angle)

Sin(/4) = (1/2 ) = -(1/2)

Cos(/4) = (1/2) = 1/2

tan (/4) =- 1

Cosec (/4)= -2

Sec (/4) = 2

Cot(/4) = -1

Again = /6 ( as a referance angle)

Sin(/6) = (1/2) = -(1/2)

Cos(/6) = (3/2)

tan (/6) = -(1/3)

Cosec (/6)= -2

Sec (/6) = 2/3

Cot(/6) = -3

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