How do you prove #sin 5pi/12 = sin pi/6 cos pi/4 + cos pi/6 sin pi/4#?

1 answer:

6 0

You rewrite 5π/12 as 2π/12 + 3π/12 since 2 + 3 = 5.
Then you simplify the fractions into π/6 + π/4.
Then you use the sine addition identity.

sin(5π/12) = sin(π/6 + π/4) = sin π/6 cos π/4 + cos π/6 sin π/4

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The diagram shows a circle centre O work out the size of angle X work out the size of angle y

bagirrra123 [75]

Answer:

x = 116° , y = 20°

Step-by-step explanation:

Since, measure of angle subtended on the center of the circle is twice the measure of angle subtended on the circumference of the circle.

$\therefore \: x = 2 \times 58 \degree \\ \huge \red{ \boxed{ \therefore \: x =116 \degree}} \\ \\$

Now, by angle sum property of a quadrilateral.

$y + (360 - 116) \degree + 38 \degree + 58 \degree = 360 \degree \\ y + 244 \degree + 96 \degree = 360 \degree \\ y + 340 \degree= 360 \degree \\ y = 360 \degree - 340 \degree \\ \huge \purple{ \boxed{ y = 20 \degree}}$