Angle – Set of points determined by two rays. Example
"name": " Angle – Set of points determined by two rays.",
Coterminal angles - two angles with the same initial and terminal sides. Straight angle – an angle whose sides line on a straight line and extend in opposite directions from the vertex. Degrees – One unit of measuring an angle. One complete revolution in the counter clockwise direction is 360*.
Using the x-y plane, the standard position of an angle has its vertex at the origin and its initial side as the positive x-axis. If the terminal angle is rotated counter clockwise, the angle is positive. If the terminal angle is rotated clockwise, the angle is negative.
Find the six trig values for θ if θ is in standard position and P(2,-5) is on the terminal side.
Find the values of x and y in the triangle below using trig functions.
You are visiting Sequoia National Park in California to see the Giant Redwood Trees. You are standing 500ft away from the biggest tree that you can find and the angle between the ground and the top of the tree is 33 *. How tall is the tree?
Recall that the unit circle has its center at (0,0) and a radius of 1. If we divide the special right triangles so the hypotenuse equals 1 we get that the points on the unit circle have coordinates.
The the coordinates on the unit circle are of the form. We get the following values for 0, 30, 45, 60, and 90 degrees.
We can see that the 6 trig functions are reciprocals of one another. Sin and Csc are reciprocals, Cos and Sec are reciprocals, and Tan and Cot are also reciprocals.
All of the identities we learned are found in the back page of your book under the heading Trigonometric Identities and then Fundamental Identities. You'll need to have these memorized or be able to derive them for this course. RECIPROCAL IDENTITIES QUOTIENT IDENTITIES PYTHAGOREAN IDENTITIES
We can verify that the following identity is true by making the left side match the right side.
Deriving the Pythagorean Identity using the Pythagorean Theorem and the unit circle.
When verifying identities, it is important to remember that all 6 trig functions can be written using sin and/or cos.
Verify the following identity by re-writing the left hand side to match the right hand side.
This video graphs all three functions simultaneously while rotating the angle in standard position on the unit circle. http://www.dnatube.com/video/12168/Trig- graphs http://www.dnatube.com/video/12168/Trig- graphs
A drawbridge is 150ft long across a river. The two sections are of equal length and can be rotated upward to an angle of 35*. If the water level is 15 feet below the bridge when it is closed. Find the distance between the end of each section of the bridge when raised and the surface of the water.
A plane is on approach to the Harrisburg Airport at a current elevation of 10000ft. If the plane is 12 miles away what angle of decent should the pilot take to land at the airport?