1. Trigonometric Calculations

2. 1.Define the trigonometric ratios using sinθ, cos θ and tan θ, using right angles triangles. 2.Extend the definitions for sinθ, cos θ and tan θ for 0°< θ<360° 3.Define the reciprocals of trigonometric ratios cosec θ, sec θ, cot θ 4.Derive values of trigonometric ratios for special cases (without using a calculator) θЄ{0 °; 30 °; 45 °; 60 °; 90 °} 5.Solve two dimensional problems involving right angled triangles. 6.Solve simple trigonometric equations for acute angles. 7.Use diagrams to determine the numerical values of ratios for angles from 0 ° to 360 °.

3. Calculator Usage Examples Determine the value of each of the following using a calculator (Round off your answer to twp decimal places). A)sin73° B)2sin20 ° + 3cos10 ° C)tan(21 ° + 36 ° )

4. continued Solutions A)sin73° =0,9563048 ≈ 0,96 C)tan(21 ° + 36 °) = tan 57° = 1,539865 ≈ 1,54 B)2sin20 °+ 3cos10 ° = 0,6840403 + 2,9544233 = 3,6384638 ≈ 3,64

5. Calculator usage To determine the angle if the ratio is given, is made possible on a calculator if you press the shift key or second function key, then the trigonometric function key. The keys sin-1,cos-1and tan-1 is used to show the inverse function.

6. Solve trigonometric equations To solve for θ in the following problem if θ is an acute angle. Tanθ = Key in the following on your calculator. 11.9; = ; shift ; tan-1; ans or = Therefore θ = 18,1°

7. Trigonometric Equations Examples 1)Solve for θ (Round off your answer to ONE decimal place) (θ is acute) a)sin θ = 0,823 b)2cos θ = 1,264 c)cos2 θ = 0,943 d)tan(θ - 25°) = 0,465 e)sin2 θ = 0,326 2

8. Solutions a) sin θ = 0,823 θ = 55,4 ° b)2cos θ = 1,264 cos θ = 0,632 θ = 50,8 ° c)cos2 θ = 0,943 2θ = 19,438371 ° θ = 9,711855° θ = 9,7°

9. continued d)tan(θ - 25°) = 0,465 θ - 25°= 24,938427° θ = 49,938427° θ = 49,9° e) sin2 θ = 0,326 2 sin2 θ = 0,652 2 θ = 40,69256357° θ = 20,34628179° θ = 20,3°

10. Test your Knowledge

11. Test your knowledge