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Lesson Topics Discussion Quiz: Class Homework

Example1

Title: Trigonometry

Grade Lesson s5-p1

Explanation: The best way to understand SAT-4 is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1 Example2

Find the value of \$csc^-1 (x − y)\$ where y ranges from (0, 2π) and cos(x + y) = 1.

Step: 1

The given expression is simplify
Here \$csc^(-1)\$ means reciprocal, so
\$csc^-1 (A) = sin (A)\$
So we really need to find: sin(x - y)

cos(x + y) = 1
\$x + y = cos^-1(1)\$
x + y = 360°
y = 360°- x
x = 360°- y

Explanation:

Simplify the expression given, then determine the value of x.

Step: 2

Find x - y
substitute x:
x - y = 360°

Use the formula:
\$sin(A - B) = sinA cosB - cosA sinB\$

Then plug the "x" value in the above formula and simplify the expression
\$sin(360°- y) cosy - cos(360°-y) siny\$
\$-sin(y) cos(y) - cos(y) sin(y)\$
\$-2sin(y) cos(y)\$
-sin2y

Explanation:

Apply the formula, substitute the value of x, and then simplify to obtain the expression as -sin2y.