Download presentation

1
**Ch:7 Trigonometric Identities and Equations**

By: Linitha and Hina

2
**7.1 Exploring Equivalent Trigonometric Functions**

Related functions with and 2 Cos ( – θ)= - cos θ Sin ( – θ) = sin θ Tan ( – θ) = - tan θ Cos ( + θ) = - cos θ Sin ( +θ) = - sin θ Tan ( +θ) = tan θ Cos ( θ)= cos θ Sin( θ)= -sin θ tan( θ)= -tan θ

3
**7.2 Compound Angle Formulas**

Addition formulas Sin (a+b) = sin a cos a + cos a sin b Cos (a+b) = cos a cos b – sin a sinb Tan (a+b) = tan a +tan b / 1- tan a tan b Subtraction formulas Sin (a-b)= sin a cos b – cos a sin b Cos (a-b) = cos a cos b +sin a sin b Tan (a-b) = tan a – tan b/ 1 + tan a tan b

4
**7.3 Double Angle Formulas Double angle formula for sine**

Sin 2θ = 2 sin θ cos θ Double angle formulas for cosine Cos 2θ = cos2 θ – sin2 θ Cos 2θ = 2 cos2 θ – 1 Cos 2θ = 1-2 sin2 θ Double angle formulas for tangent Tan 2θ = 2 tan θ / 1- tan2 θ

5
**7.4 Proving Trigonometric Identities**

Reciprocal identities Csc x= 1/ sin x Sec x= 1/cos x Cot x = 1/tan x Quotient identities Tan x = sinx / cos x Cot x= cos x/ sinx Pythagorean identities Sin 2 x + cos 2 x = 1 1 + tan 2 x = sec 2 x 1+ cot x = csc 2 x Double angle formulas Sin 2x = 2 sin x cos x Cos 2x = cos2x– sin2 x Cos 2x = 2 cos2 x – 1 Cos 2x = 1-2 sin2 x Tan2x = 2 tan x/ 1- tan2x Addition /subtraction formulas Sin (x+y) = sin x cos y + cos x sin y Cos (x+y) = cos x cos y – sin x sin y Tan (x+y) = tan x +tan y / 1- tan x tan y Subtraction formulas Sin (x-y)= sin x cos y – cos x sin y Cos (x-y) = cos x cos y +sin x sin y Tan (x-y) = tan x – tan y/ 1 + tan x tan y

6
**7.5 Solving Linear Trigonometric Equations**

Special Triangles CAST Rule Calculator (only when not in special triangle) Period of the function so the number of solutions are known in the specified interval

7
**7.6 Solving Quadratic Trigonometric Equations**

Factoring Quadratic Formula Sin2 x – sinx = 2 Sin2 x – sinx – 2 = 0 ( sinx – 2) (sinx + 1) = 0 Sinx = or sinx = -1 No solution x = 3 2 (0, -1)

8
Question Time!!!

9
1. Use the co function identities to write an expression that is equivalent to each of the following expressions. Sin 6 Tan 3 8 Cos 5 18

10
**2. State whether each of the following are true or false**

Cos (θ +2 )= cos θ Sin ( - θ) = -sin θ Cot ( θ)= tan θ 2

11
**3. Determine the exact value of**

A) Cos (15 °) B) tan(-5 /12) 4. simplify each expression A) cos 7 /12 cos 5 /12 + sin 7 /12 sin 5 /12 B) sin 2x cos x – cos 2x sin x

12
**5. Simplify each of the following expressions and then evaluate**

A) 2 sin /8 cos /8 B) 2 tan /6 / 1 – tan 2 /6

13
**6. If cosθ = -2/3 and 0 < θ < 2pie , determine the value of cos 2θ and sin 2θ**

7. Develop a formula for sin x/2

14
**8. prove that sin 2x / 1 + cos2x = tan x**

9. prove that sin x + sin 2x = sin 3x is not an idenitity 10. prove that cos ( /2 + x) = - sin x

15
**11. Cos (x - y)/ cos (x + y) = 1 + tan x tan y/ 1- tan x tan y**

12.Prove that tan 2x – 2 tan 2x sin2 x = sin 2x 13. prove that 1 + tan x / 1 + cot x = 1- tan x /cot x - 1

16
**14. Determine all solutions in the specified interval for the following equation:**

0 < x < 2 2sinx + 1 = 0

17
15. Use a calculator to determine the solutions for the following equation on the interval 0 < x < 2 2 – 2cotx = 0

18
**16. Solve the equation for x in the interval 0 < x < 2**

2sin2x – 3sinx + 1 = 0

19
**17. Use a trigonometric identity to create a quadratic equation**

17. Use a trigonometric identity to create a quadratic equation. Then solve the equation for x in the interval [0, 2 ] 2sec2 x – 3 + tanx = 0

Similar presentations

OK

Then/Now You used sum and difference identities. (Lesson 5-4) Use double-angle, power-reducing, and half-angle identities to evaluate trigonometric expressions.

Then/Now You used sum and difference identities. (Lesson 5-4) Use double-angle, power-reducing, and half-angle identities to evaluate trigonometric expressions.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on facebook graph search Ppt on airport management system Ppt on natural numbers 0 Free ppt on crop production and management Ppt on working of ac generator Ppt on mobile computing from iit bombay Time of flight ms ppt online 2d viewing ppt on ipad Ppt on boilers operations management Ppt on the road not taken audio