SaiBook.us SAT-2

Lesson Example Discussion Quiz: Class Homework

Example

Title: Trigonometry Identities (quotient , co-function)

Grade: 1400-a Lesson: S3-L4

Explanation: The best way to understand SAT-2 is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

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

Step 1a

The given expression is simplify
⇒ 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 1b

Use the formula:
\$"sin"("x" - "y") = "sinx" "cosy" - "cosx" "siny"\$
\$"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")\$
⇒ \$-2"sin"("y") "cos"("y")\$
⇒ \$- sin2y\$

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