7.4 Basic Trig Equations.pptx
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This document discusses solving trigonometric equations. It explains that trigonometric equations contain trigonometric functions and can be solved using algebra by finding the values of theta that make the equation true. Examples are provided to demonstrate solving equations involving sin, cos, and tan. Factoring can also be used to help solve trigonometric equations, as shown in an example of solving an equation involving cos^2. Practice problems are included at the end.
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- 1. 7.4 BASIC TRIG EQUATIONS PG. 564
- 2. RECALL (SUM-PRODUCT FORMULA PG. 560)
- 3. INTRODUCTION PG. 564 An equation that contains trigonometric functions is called a trigonometric equation. For example, the following are trigonometric equations: 𝑠𝑖𝑛2 𝜃 + 𝑐𝑜𝑠2 𝜃 = 1 2 sin 𝜃 − 1 = 0 tan 2𝜃 − 1 = 0
- 4. BASIC TRIGONOMETRIC EQUATIONS PG. 564 Solving any trigonometric equation involves finding what value of 𝜃 would make the equation true We do this by using algebra and all of the other techniques we’ve learned to solve equations
- 5. EXAMPLE 1 PG. 564 Solve the equation sin 𝜃 = 1 2
- 6. EXAMPLE 1 PG. 564 Solve the equation sin 𝜃 = 1 2
- 7. EXAMPLE 2 PG. 565 Solve the equation cos 𝜃 = − 2 2 , and list 8 specific solutions
- 8. EXAMPLE 2 PG. 565 Solve the equation cos 𝜃 = − 2 2 , and list 8 specific solutions
- 9. EXAMPLE 5 PG. 567 Find all solutions of the equations A) 2 sin 𝜃 − 1 = 0 B) tan2𝜃 − 3 = 0
- 10. SOLVING TRIG EQUATIONS BY FACTORING PG. 567 Just like we can solve equations using factoring, we can also use factoring to solve trig equations
- 11. EXAMPLE 6 PG. 567 Solve the equation 2cos2 𝜃 − 7 cos 𝜃 + 3 = 0
- 12. SUMMARY In order to solve trig equations, we first find the solutions in one period of the function, 0 ≤ 𝜃 ≤ 2𝜋 We then use these solutions to find all solutions We can also use factoring to help us solve trig equations
- 13. PRACTICE Pg. 569 8, 20, 32, 42, 54