WordPress.com



GRADE:10 TRIGONOMETRY CHAPTER: 7SINE RULE????COSINE RULE?AREA OF A TRIANGLE.?Sine, Cosine and TangentThe three main functions in trigonometry are Sine, Cosine and Tangent.For an angle θ, the functions are calculated this way:Sine Function:?sin(θ) = Opposite / HypotenuseCosine Function:?cos(θ) = Adjacent / HypotenuseTangent Function:?tan(θ) = Opposite / AdjacentFour QuadrantsWhen we include negative values, the x and y axes divide the space up into 4 pieces: Quadrants I, II, III and IV(They are numbered in a counter-clockwise direction)In Quadrant I both x and y are positive, in Quadrant IIx is negative (y is still positive), in Quadrant IIIboth x and y are negative, andinQuadrant IV x is positive again, and y is negative. Sine, Cosine and Tangent in the Four Quadrants Now let us look at what happens when we place a 30° triangle in each of the 4 Quadrants.In Quadrant I everything is normal, and Sine, Cosine and Tangent are all positive: Example: The sine, cosine and tangent of 30°But in Quadrant II, the x direction is negative, and both cosine and tangent become negative:Example: The sine, cosine and tangent of 150°In Quadrant III, sine and cosine are negative:Example: The sine, cosine and tangent of 210°In Quadrant IV, sine and tangent are negative:Example: The sine, cosine and tangent of 330°There is a pattern! Look at when Sine Cosine and Tangent are positive ...All three of them are positive in Quadrant ISine only is positive in Quadrant IITangent only is positive in Quadrant IIICosine only is positive in Quadrant IV Two ValuesThere are two angles (within the first 360°) that have the same value!And this is also true for Cosine and Tangent.First valueSecond valueSineθ180? ? θCosineθ360? ? θTangentθθ ? 180?And if any angle is less than 0?, then add 360?.We can now solve equations for angles between 0? and 360? (using Inverse Sine Cosine and Tangent)Example: Solve sin θ = 0.5We get the first solution from the calculator = sin-1(0.5) = 30? (it is in Quadrant I)The other solution is 180? ? 30? = 150? (Quadrant II)Example: Solve?tan θ = ?1.3We get?the first solution from the calculator = tan-1(?1.3) = ?52.4? This is less than 0?, so we add 360?: ?52.4? + 360? = 307.6? (Quadrant IV)The other?solution is?307.6? ? 180?? = 127.6? (Quadrant II)Example: Solve?cos θ = ?0.85We get?the first solution from the calculator = cos-1(?0.85) = 148.2? (Quadrant II)The other solution is 360? ??148.2? = 211.8? (Quadrant III)x--------------x------------x ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download