Answering the trigonometric examples is nothing but we are solving the trigonometric functions and trigonometric identities. Here we will take trigonometric functions and equations. Trigonometric examples contain trigonometric functions. In trigonometric model we will solve the Sin, Cos, Tan Identities. We can find the angles from these identities. We will solve some trigonometric examples.
Explanation for Solving Trigonometric Examples:
Ex 1: Solve the following trigonometric equation Cos4A – Sinn 2A =0
Sol : Cos 4A – sin2A =0
2Sin2 (2A) + Sin (2A) – 1 = 0
Here we can use quadratic formula to find A value. Let us take any variable equal to Sin 2A
Let us take y = Sin 2A
2y2 + y – 1 =0
2y2+2y – y – 1 = 0
2y(y + 1) – (y + 1) = 0
If we factor this we will get two values for y.
(y + 1)(2y – 1) = 0
Now y + 1 = 0 2y – 1 = 0
Now plug y = Sin2A
Sin 2A + 1 = 0 2Sin2A – 1 =0
Sin 2A = -1 2Sin 2A = 1
2A = Sin-1 (-1) Sin 2A =
2A = 270 2A = Sin-1
2A = 30
A = 135 A = 15
From this we will get two value for A.
Practice Problem for Solving Trigonometric Examples:
Ex 2: Solve the assessment of the following trigonometric identity Sin 75 - Cos 15
Sol : Sin 75 – Cos 15
Here we have to use sum and variation formula to find the value os Sin 75 - Cos 15
Sin (45 + 30) – Cos (45 - 30)
Sin (A + B) = Sin A Cos B + Cos A Sin B
Cos (A - B) = Cos A Cos B + Sin A Sin B
Here A = 45
B = 30
Sin (45 + 30) = Sin45.Cos30 + Cos45Sin30
= 0.7071 * 0.8660 + 0.7071 * (0.5)
= 0.6123 + 0.3536
Sin 75 = 0.9659
Cos (45 – 30) = Cos45Cos30 + Sin45Sin30
=0.7071 * 0.8660 + 0.7071 * (0.5)
=0.6123 + 0.3536
Cos 15 = 0.9659
Now plug the values in the equation is
Sin 75 – Cos15 = 0.9659 – 0.9659
Sin 75 – Cos15 = 0
Ex 3: Solve for x Sin x = 0.5, Cos x = 0.8660
Sol : (I) Given Sin x = 0.5
x = Sin-1 (0.5)
x = 30o
(II) Cos x = 0.8660
x = Cos-1 (0.8660)
x = 300
So from this angle x =30o. Here we use the opposite trigonometric functions to find the value of x.
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