Trigonometry Problems and Solutions with Graphs
Explore trigonometry problems and solutions using graphs for sine and tangent functions. Solve various trigonometric equations, such as finding angles and values, with the help of visual representations. Enhance your understanding of trigonometry concepts with step-by-step explanations and graphical illustrations.
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Presentation Transcript
Here is the graph of ? = sin? What are the solutions to sin? = 1? There are an infinite number of solutions so the domain must be specified.
Using your graph of ? = sin? Solve sin? = 0.5 ,0 ? 360 Notice that this distance is equal due to the symmetry of the curve.
Using your graph of ? = sin? Solve sin? = 0.5 ,0 ? 360 Notice that this distance is equal due to the symmetry of the curve.
Using your graph of ? = tan? ? = 180 + 16.7 ? = 196.7 (1 dp) ? = ??? 10.3 ? = 16.7 (1 dp) Solve tan? = 0.3 ,0 ? 360 Here the value is difficult to read from the graph exactly. How can we use our calculator to help?
Using your graph of ? = tan? 26.6 26.6 Solve tan? = 0.5 ,180 ? 360 ??? 1 0.5 = 26.6
Discuss: How could we solve 5sin? = 2 ??? 0 ? 360 using the graph of ? = sin? ?
Using your graph of ? = sin? Solve sin? = 0.4 ,0 ? 360
Using your graph of ? = sin? Solve sin? = 0.4 ,0 ? 360
Using your graph of ? = sin? sin? = 0.85 and angle A is obtuse Work out angle A
In your books: Give your answers to 3 significant figures 1. Solve cos? = 0.4 for 0 ? 360 2. Solve cos? = 0.2 for 180 ? 360 3. Solve cos? + 1 = 1.9 for 0 ? 360 4. Solve 2???? = 1 for 0 ? 360
Mark your work 1. 66.4, 294 2. -102, 102, 258 3. 25.8, 334 4. 120, 240
Challenge Solve 4???2? 1 = 0 for 0 ? 360
Mark your work -30, 210, 330 30, 150
