Trigonometry-when to use cos and when to use sin.

Now it is not necessary to construct a unit circle all the time when dealing with trigonometry.

When given an angle and asked to find the length of one of the sides of a right angle triangle it is importnat to know if the side is adjacent or opposite to the angle given.

If the side is opposite we use sin.

If the side is adjacent we use cos.

Remembering back to our similar triangles here are two simple formulae that are necessary for the problems here.

hypotenuse X sin(xo) = opposite

hypotenuse X cos(xo) = adjacent

Find the length of "y"

Step 1 Identify if "y" is opposite or adjacent the angle given.

Step 2 Use a calculator (your computer has one) to find the value of sin(30o).
Type in 30 in your calculator and press sin
The value of sin(30o) should appear as 0.500

Step 3 Use the appropriate formula to solve for "y"

Find the length of "y"

Step 1 Identify if "y" is opposite or adjacent the angle given.

Step 2 Use a calculator (your computer has one) to find the value of cos(60o).
Type in 60 in your calculator and press cos
The value of cos(60o) should appear as 0.500

Step 3 Use the appropriate formula to solve for "y"

Calculate "x"

Solution
Solution
Solution

Find the shaded area.

Step 1 Identify the shapes that make up the shaded region.

Step 2 Find the dimensions of each shape.

Step 3 Calculate the area