Compound Angle Formulae

Summary Compound angle formulas are: Half angle formulas are: Function to trigonometric form: In Fig 1, and are acute angles and As Hence, Replacing B by -B in i) Also from the diagram: Hence, Also: We have derived the compound angle formulae above. All the compound angle formulas are listed below: Double Angle formulae We … Read more

Solving Trigonometric Equations

Summary To solve trigonometric equations, several identities and formulas are used i.e: For basic trigonometric equations, we follow the following steps to solve them: 1.    Make sine, cosine or tangent the subject. 2.    Use any method including a calculator to find basic angles. 3.    Using quadrants, find all solutions in the given range. Example #1 … Read more

Sin, Cos and Tan

Summary First Quadrant: All are positive in this quadrant. Second Quadrant: Only sin is positive in this quadrant. Third Quadrant: Only tan is positive in this quadrant. Fourth Quadrant: Only cos is positive in this quadrant.   We now consider angles in cartesian plane. We divide the plane into four quadrants in the anticlockwise sense … Read more

Sec, Cosec and Cot

Summary Secant (sec) is the reciprocal of cosine (cos): Cosecant (cosec) is the reciprocal of sin: Cotangent (cot) is the reciprocal of tan: Recall, in case of a right angle triangle if we are given one length and one angle and we have to find a missing length or if we need to find a … Read more

Radians

Summary 1 Revolution = 360° radian = 180° 1 radian = = 57.3° 1° =  radian  = 0.175 radian Length of arc  Area of a Sector   Area of a segment   The most common system of measuring the angles is that of degrees. One complete revolution is divided into 360 equal parts and each part is … Read more

Sine and Cosine Rule

Summary Pythagoras theorem: only for right angle triangles:   For other triangles: 1.    Sine Rule: or 2.    Cosine Rule: or Area of a triangle :  Let’s quickly go back and recall the pythagoras theorem. We know that for any right angle triangle, if we have got lengths of two given sides, we can find the length … Read more