Simplify the Resulting Expression - Function Values of Common Angles from a Table

Question

sin 60 degrees cos 45 degrees + cos 60 degrees sin 45 degrees

Where to even begin? There is a table called "Trigonometric function Values of some common angles" in the textbook that we are to use to find the answer.

Answer 1

Begin by drawing two right triangles.

The first is isosceles with base angles of 45° Mark the hypotenuse as 1.

Calculate by Pythagoras the lengths of the two equal sides.

You can now list the functions of 45°/

The second is a 30-60-90 triangle (just a sketch shall do).

Mark the hypotenuse as 1.

The side opposite the 30° angle is 1/2. Mark it.

Calculate the third side using Pythagoras.

You can now list the functions for 30° and 60°

These values "pop-up" a lot in Trigonometry. Learn them by heart of how to quickly derive them from the triangles.

Answer 2

Look up the values of sin 60, cos 60, sin 45, cos 45. Put the values into the equation, and solve!

Answer 3

sin60°cos45° + cos60°sin45° = (√3/2)(√2/2) + (1/2)(√2/2) = [√6 + √2] / 4