Trigonometry
Trigonometry
Defining Trigonometric Functions
- Understand sine (sin), cosine (cos), and tangent (tangent) as ratios of the sides in a right-angled triangle.
- Illustrate the definition of trigonometric functions on the unit circle, where radius = 1.
- Apply the SOHCAHTOA mnemonic to remember the definitions of sin, cos, and tan.
Trigonometric Identities
- Comprehend the Pythagorean Identity, which is sin²x + cos²x = 1.
- Recognise that tanx is equivalent to sinx/cosx.
- Understand and apply the double angle formulae for sin2x, cos2x and tan2x.
- Implement the reciprocal identities: secx=1/cosx, cscx=1/sinx, cotx=1/tanx.
Solving Trigonometric Equations
- Solve basic trigonometric equations for given intervals, using radian and degree measures.
- Make use of standard results to solve trigonometric equations involving multiples of 30° or 45° or 60° or 90°.
- Use trigonometric identities to simplify and solve more complex equations.
- Understand how to sketch the trigonometric functions and use these sketches to solve associated equations.
Trigonometric Values of Special Angles
- Memorise the exact values of sin, cos and tan for 0°, 30°, 45°, 60° and 90°.
- Use symmetries of the trigonometric functions to identify corresponding values for angles over 90°.
Trigonometric Applications
- Utilise trigonometry to find distances and angles in right-angled triangles.
- Apply trigonometry to solve practical problems involving angles of elevation and depression.
- Comprehend and calculate the area of a triangle using 1/2absinC.
- Use the sine and cosine rules to solve problems involving non-right angled triangles.
Trigonometric Graphs
- Understand how to graph y=sinx, y=cosx, and y=tanx.
- Identify the amplitude, period, phase, and shifts for the given trigonometric graphs.
- Understand the effect of changing the coefficient of x on these graphs.