Unit 1:
Summary:
Although it would be easier just to check the unit circle for degree and radian measurements, that does not work for all the measurements. As long as either the pi or degrees are fixed to cancel out in the equation, its pretty easy to convert. Radians and degrees are just two ways to measure angles.
Although it would be easier just to check the unit circle for degree and radian measurements, that does not work for all the measurements. As long as either the pi or degrees are fixed to cancel out in the equation, its pretty easy to convert. Radians and degrees are just two ways to measure angles.
Sine and Cosine:
Summary:
Sine and Cosine are related to the Pythagorean Theorem. They are a way to demonstrate the relationship between coordinates on a graph or sides of triangles and the unit circle. Ways of measurements are demonstrated in different ways to make it easier to understand and available when solving different problems. The original sine and cosine graphs will always match the unit circle unless the amplitude is changed, in which case the frequency of the waves will also.
Sine and Cosine are related to the Pythagorean Theorem. They are a way to demonstrate the relationship between coordinates on a graph or sides of triangles and the unit circle. Ways of measurements are demonstrated in different ways to make it easier to understand and available when solving different problems. The original sine and cosine graphs will always match the unit circle unless the amplitude is changed, in which case the frequency of the waves will also.
Finding Unknown Sides of Right Triangles
- To find the unknown sides of a right triangle use the trigonometric functions: tanΘ= opposite/ adjacent
& cosΘ= adjacent/ hypotenuse
- Or the inverse trigonometric functions: cotangentΘ= adjacent/ opposite
& cosecantΘ= hypotenuse/adjacent
Using the Trig Functions
- For Example:
- Suppose you want to climb a hill, you know the distance climbing up the hill (Hypotenuse= 30 feet) and you know the angle your looking at it from (angle A= 70°)
- Supposing your at angle A, and want to find out how tall the hill is, use the trig inverse function sine
(multiply by 30) → Opp. = 28.2 Feet
- The hill is about 28.2 feet away
- Trigonometric functions work best when knowing a side of a triangle and an angle. They make fun word problems and can lead to knowing all three sides of a triangle through the formula a^2+ b^2= c^2.