Term 3 : Unit 1 Trigonometry (Part B) Name : ____________ ( ) Class : ______ Date :________ 1.3 Simple Identities 1.4 Trigonometric Equations

Simple Trigonometric Identities and Equations 1.3 Simple Identities In this lesson, we will define the secant, cosecant and cotangent functions, learn some simple trigonometric identities. Objectives

Trigonometric Ratios of Acute Angles The three trigonometric ratios are defined as OPQ is a right angled triangle. adjacent opposite hypotenuse opposite hypotenuse adjacent Simple Trigonometric Identities and Equations

Consider angles in the Cartesian plane. Simple Trigonometric Identities and Equations For any value of θ. r 2 = x 2 + y 2

Simple Trigonometric Identities and Equations

From the identity Rearrangin g Example 3

Simple Trigonometric Identities and Equations Rearranging 1 + cot 2 x = cosec 2 x Using the identities Cancelling Example 1

Simple Trigonometric Identities and Equations Using the identity Example 2

Simple Trigonometric Identities and Equations Using the identity 1 + cot 2 x = cosec 2 x. Example 3

Simple Trigonometric Identities and Equations Using the identity. Example 4

Simple Trigonometric Identities and Equations 1.4 Trigonometric Equations In this lesson, we will solve some further trigonometric equations by simplifying or factorising, to reduce them to the form sin x = k, cos x = k and tan x = k. Objectives

Find all the angles between 0° and 360° which satisfy the equation 3 cos x + 2 sin x = 0. Simple Trigonometric Identities and Equations cos x ≠ 0 tan x < 0 so x is in the 2nd or the 4th quadrant. Using the identity. Calculate the base angle α. Example 5

Find all the angles between 0 o and 360 o which satisfy the equation sin y = 4 tan y. Simple Trigonometric Identities and Equations Using the identity Factorise, do not cancel through by sin θ. No solutions –1 ≤ θ ≤ 1 Example 6

Find all the angles between 0° and 360° which satisfy the equation 2 cos 2 y – 1 = sin y. Simple Trigonometric Identities and Equations Using sin 2 y + cos 2 y = 1 sin y > 0 so y is in the 1st or the 2nd quadrant. Factorisin g Example 7

Find all the angles between 0° and 360° which satisfy the equation cos (x + 30 o ) = – 0.3. Simple Trigonometric Identities and Equations cos (x + 30°) < 0 so x is in the 2nd or the 3rd quadrant. Calculate the basic angle α. Example 8

Find all the angles between 0° and 360° which satisfy the equation sin 2x = Simple Trigonometric Identities and Equations sin 2x > 0 so x is in the 1st or the 2nd quadrant. Calculate the basic angle α. Example 9