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45-45-90 Right Triangles

45-45-90 Right Triangles. Consider the following 45-45-90 right triangle. Since the triangle is isosceles, the sides opposite the 45 ° angles are equal in measure . Assign a value of 1 to each side. Use the Pythagorean Theorem to determine the length of the hypotenuse.

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45-45-90 Right Triangles

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  1. 45-45-90 Right Triangles • Consider the following 45-45-90 right triangle. • Since the triangle is isosceles, the sides opposite the 45° angles are equal in measure. Assign a value of 1 to each side.

  2. Use the Pythagorean Theorem to determine the length of the hypotenuse.

  3. This 45-45-90 right triangle can give us the trigonometric function values of 45°.

  4. Recall that on the unit circle we have … • This leads us to some important values on the unit circle.

  5. Since (a,b) = (cos 45°, sin 45°) , we have • Consider the point (a,b) on the 45° ray of a unit circle.

  6. In radian form it would be …

  7. Moving around the unit circle with reference angles of π/4 we have …

  8. Example 1: • Find cos 3π/4 • Since cosx is equal to the first coordinate of the point we have …

  9. Example 2: • Find sin 5π/4 • Since sin x is equal to the second coordinate of the point we have …

  10. Example 3: • Find tan (-3π/4) • Since tan x is equal to b/a we have …

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