Show trigonometric functions on a graph, Mathematics

Assignment Help:

Q. Show Trigonometric Functions on a Graph?

Ans.

By discussing the trig functions with respect to an angle in a right-angle triangle, we have only considered angles between 0o and 90o. What about angles of 90o and larger?

For simplicity, lets concentrate on the unit circle. When the angle is between zero and ninety degrees, we can use a triangle to help us find sine, cosine and tangent of the angle.

2125_Show Trigonometric Functions on a Graph.gif

From this diagram, you can see that sinθ = y , cosθ = x and tan θ = y/x when 0o< θ<90o or 0 < θ < Π.

We can use everything we know about angles between 0 and Π/2 , to find the values of sine, cosine and tangent of ALL angles! 
(Remember that we are only dealing with points on the unit circle at the moment!)

Let's consider all four quadrants of the Cartesian plane.

214_Show Trigonometric Functions on a Graph1.gif

First consider the second quadrant with angles between 90o and 180o.

34_Show Trigonometric Functions on a Graph3.gif

The angles θ and Φ are related as follows:

1299_Show Trigonometric Functions on a Graph4.gif

Since 0o < Φ < 90o we can use a right-angle triangle to find sinΦ.

1922_Show Trigonometric Functions on a Graph5.gif

sinΦ = y , cosΦ = x and tanΦ = y/x BUT notice that in this quadrant, x is negative! Thus cos Φ and tan Φ are both negative, but sin Φ is positive.

This is all well and good, but why are we looking at sin Φ when all we want to know is sinθ ?WHY?

Thus sin θ = sin(Π -θ), cos θ = -cos (Π -θ) and tan θ = -tan (Π -θ)

In fact, aside from the first quadrant, all the other quadrants have only one of sine, cosine or tangent positive.

sin θ is positive in the second quadrant.

tan θ is positive in the third quadrant.

cos θ is positive in the fourth quadrant.

Although we restricted ourselves to all the points on the unit circle, the trigonometric functions are dependent purely on the angle. Thus we now know the sine, cosine and tangent of every angle

2466_Show Trigonometric Functions on a Graph6.gif

The following picture shows which functions are positive in the four quadrants.

887_Show Trigonometric Functions on a Graph7.gif

Here is a simple way to help you remember this information. Write the word CAST counter-clockwise beginning in the fourth quadrant. These letters symbolize which functions are positive.

2231_Show Trigonometric Functions on a Graph8.gif


Related Discussions:- Show trigonometric functions on a graph

Sum and difference identities, Q. Sum and Difference Identities? Ans. ...

Q. Sum and Difference Identities? Ans. These six sum and difference identities express trigonometric functions of (u ± v) as functions of u and v alone.

Pair of straight line, The equation ax2 + 2hxy + by2 =0 represents a pair o...

The equation ax2 + 2hxy + by2 =0 represents a pair of straight lines passing through the origin and its angle is tan q = ±2root under h2-ab/(a+b) and even the eqn ax2+2hxy+by2+2gx+

Permission for xii class, Is there any class in expertsmind for second year...

Is there any class in expertsmind for second year english.?

Trignometric Equations, Equation for the given intervaks in the intervaks, ...

Equation for the given intervaks in the intervaks, giving ypout answer correct to 0.1 1.sin x = 0.8 0 2. cos x =-0.3 -180 3.4cos theta- cos theta=2 0 4. 10tan theta+3=0 0

Demerits and merit-the geometric mean , The geometric mean Merits ...

The geometric mean Merits i.  This makes use of all the values described except while x = 0 or negative ii.   This is the best measure for industrial increase rates

Compute the probability of event, 1) Let the Sample Space S = {1, 2, 3, 4, ...

1) Let the Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8}. Suppose each outcome is equally likely. Compute the probability of event E = "an even number is selected". P(E) = 2) A s

What is graphing statistics explain , What is Graphing Statistics explain ?...

What is Graphing Statistics explain ? The number of times that an event occurs is called its frequency. One of the ways that you can compare or display different frequencies is

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd