This week in Advanced Math we were introduced to Chapter 7. This chapter included angles, arcs, sectors, the sine and cosine functions, and also the tangent, secant, cotangent, and cosecant trigonometric functions. In lesson 7-3 we were taught how to use sine and cosine to find values of these functions and solve simple trigonometric equations.
-Sine of Ѳ is defined sinѲ
sin is defined in the coordinate plane as:
y → sin
r/hypotenuse → radius/ a²+b²=c²
-Cosine of Ѳ is defined cosѲ
cos is defined in the coordinate plane as:
x → cos
r/hypotenuse → radius/ a²+b²=c²
-Sin is positive in the quadrant where (y) is positive and vice versa.
-Cos is positive in the quadrant where (x) is positive and vice versa.
Example: If the terminal ray of angle α in standard position passes through (-2, 4) find sinѲ and cosѲ.
sinѲ=(-2)/(2√5) =(2√5)/(2√5)= (-4√5)/(5)
cosѲ=(-4)/(2√5) =(2√5)/(2√5)= (-8√5)/(5)
The key to Chapter 7 is learning the formulas. If you know your formulas, the process becomes much easier to work through.
The thing that tripped me up on this lesson was making sure the bottom number was rationalized. Remember to rationalize and complete each step of the process.
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