Trigonometry 2

Subject 1: The functions SIN, COS and TAN on the real line, radians.

• Level 1: Identifying points on the unit circle
• Level 2: Finding a number verifying SINx<0 and COSx>0
• Level 3: Finding the value of SINx given COSx and x in quadrant IV
• Level 4: Verifying the truth of a sentence
• Level 5: The length of an arc and the area of a sector 

Subject 2: The Formulas for SIN(x + y), SIN(2x), etc.

• Level 1: Calculate the exact values of SIN(15^o), COS(105^o)
• Level 2: Express SIN(x/4) in terms of COS(x/2)
• Level 3: Express SIN(3x) in terms of SIN(x)
• Level 4: Express (SIN(3x) + SIN(x)) / (COS(3x) + COSx) as a function of (2x)

Subject 3: Conversions of sums to products, of aSIN(x) + bCOS(x)to cSIN(x+y)

• Level 1: Express COS(x) - COS(2x+y) as a product
• Level 2: Express 2SIN(x) - 3COS(x) as a product
• Level 3: Express 2SIN(x) + 3COS(x) in the form kSIN(x + a)

Subject 4: Solving trigonometric equations.

Find all the solutions of the following equations:
• Level 1: 2COS(x) + 3 = 0
• Level 2: 3TANx-2 = 0 in the interval [-2,2]
• Level 3: SIN(3x) = 0.6
• Level 4: 4COS(2x)+1 = 0 in the interval [-1,1]
• Level 5: 3COSx+SIN(2x) = 1