Trignometry - Formulas and Properties

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In a right-angled triangle, we consider an angle 'x'

Sin(x) = $$\dfrac{opposite}{hypotenuse}$$

Cos(x) = $$\dfrac{adjacent}{hypotenuse}$$

Tan(x) = $$\dfrac{opposite}{adjacent}$$

Trigonometric values for important angles: 0, 30, 45, 60, 90.

Sin(0) = 0, Sin(30) = 1/2, Sin(45) = 1/$$\sqrt{\ 2}$$, sin(60) = $$\frac{\sqrt{\ 3}}{2}$$, sin(90) = 1 

Cos(0) = 1, Cos(30) = $$\frac{\sqrt{\ 3}}{2}$$, cos(45) = 1/$$\sqrt{\ 2}$$, cos(60) = 1/2, cos(90) = 0

Tan(0) = 0, Tan(30) = $$\frac{1}{\sqrt{\ 3}}$$, Tan(45) = 1, Tan(60) = $$\sqrt{\ 3}$$, Tan(90) = infinity.

Sin(90+x) = cos(x)

Cos(90+x) = -sin(x)

sin(-x) = -sin(x)

cos(-x) = cos(x)

$$\sin^2\left(x\right)+\cos^2\left(x\right)=1$$

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

cos(x+y) = cos(x)cos(y) - sin(x)sin(y)

Question 1

The angle of elevation of a ship to a lighthouse changes from 30 degrees to 45 degrees in 15 minutes. How much more time does the ship take to reach the lighthouse?

Question 2

Two lamp posts of equal height are 200 metres apart. The angles of elevation to the top of the two lamp posts from a point on the line joining them are 30 and 60 degrees. How far is the point to the lamp post whose angle of elevation is 30 degrees?

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