Drawing a right triangle to simply the given expressions

In summary, to solve the equation Cos(Tan^-1(x)), you can draw a right triangle with an angle whose tangent is x and use the Pythagorean theorem to find the hypotenuse. For the equation Sin(sec^-1(sqrt(x^2+16)/4)), the answer is x^2-1, as discussed in the "Precalculus homework" section.
  • #1
Johnyi
42
0

Homework Statement



Cos(Tan^-1(x))

Homework Equations


The Attempt at a Solution


Dont know how drawing a right triangle would do anything, don't know what to plug in.
 
Physics news on Phys.org
  • #2
Johnyi said:

Homework Statement



Cos(Tan^-1(x))

Homework Equations


The Attempt at a Solution


Dont know how drawing a right triangle would do anything, don't know what to plug in.

Draw a triangle with an angle whose tangent is x. Any one. For example, opposite side equals x and adjacent side equals 1. Then find the hypotenuse using the pythagorean theorem.
 
  • #3
Have another question for a whole new problem...did not want to start a new thread because i felt some people would think i would be spamming.
1. Homework Statement
Sin(sec^-1(sqrt(x^2+16)/4))

2. Homework Equations
3. The Attempt at a Solution
I did the math and ended up getting x^2-1 as the opposite, but the answers on the back of the book say other wise.
 
  • #4
Bump!
 
  • #5
This was answered in the "Precalculus homework" section.
 

Related to Drawing a right triangle to simply the given expressions

1. How do I draw a right triangle to simply the given expressions?

To draw a right triangle, you will need a ruler, a protractor, and a pencil. Start by drawing a horizontal line for one side of the triangle. Then, using your protractor, draw a perpendicular line from one end of the horizontal line to create a 90-degree angle. Finally, use your ruler to connect the two endpoints of the lines to complete the right triangle.

2. What are the steps to simplify a given expression using a right triangle?

The first step is to identify the given expression and determine if it is a trigonometric function, such as sine, cosine, or tangent. Next, draw a right triangle and label the sides according to the given expression. Then, use the Pythagorean theorem and trigonometric identities to simplify the expression. Finally, substitute the values of the sides back into the original expression to get the simplified form.

3. Can drawing a right triangle really simplify an expression?

Yes, drawing a right triangle and using the Pythagorean theorem and trigonometric identities can help simplify complicated expressions involving trigonometric functions. It allows us to visualize the relationship between the sides of a right triangle and use that information to simplify the expression.

4. Are there any shortcuts to drawing a right triangle for simplifying expressions?

Yes, there are some shortcuts you can use to draw a right triangle. For example, if the given expression involves sine or cosine, you can draw a triangle with a hypotenuse of 1 and use the values of the opposite and adjacent sides to simplify the expression. Additionally, if the expression involves tangent, you can draw a triangle with a leg of 1 and use the values of the opposite and adjacent sides to simplify the expression.

5. How can I check if my simplified expression is correct?

You can check your simplified expression by substituting the values of the sides of the right triangle back into the original expression and comparing it to the given expression. If both expressions are equal, then your simplified expression is correct. You can also use a calculator to evaluate both expressions and compare the results.

Similar threads

  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
5
Views
2K
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
2K
  • Calculus and Beyond Homework Help
Replies
8
Views
2K
Replies
6
Views
7K
  • Precalculus Mathematics Homework Help
Replies
9
Views
2K
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
30
Views
3K
  • Calculus and Beyond Homework Help
Replies
5
Views
3K
Back
Top