What are the Trigonometric Cofunction Identities?

Note:

Keywords:

definition
trig identities
trig identity
sine
cosine
tangent
cofunction identities
cofunction identity

Background Tutorials

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
- What are Acute, Obtuse, Right, and Straight Angles?
  
  Did you know that there are different kinds of angles? Knowing how to identify these angles is an important part of solving many problems involving angles. Check out this tutorial and learn about the different kinds of angles!
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
- What are Acute, Obtuse, and Right Triangles?
  
  Did you know that there are different kinds of triangles? Knowing how to identify these triangles is an important part of solving many problems involving these triangles. Check out this tutorial and learn about some of the different kinds of triangles!
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
- What is the Substitution Property of Equality?
  
  If you ever plug a value in for a variable into an expression or equation, you're using the Substitution Property of Equality. This property allows you to substitute quantities for each other into an expression as long as those quantities are equal. Watch this tutorial to learn about this useful property!
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
- What is the Triangle Sum Theorem?
  
  When you're dealing with triangles, the Triangle Sum theorem can be very useful in finding interior angle measurements. In this tutorial, learn how to find this helpful theorem!
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
- What are the Legs and Hypotenuse of a Right Triangle?
  
  Looking for some terminology used with right triangles? Then this tutorial was made for you! In this tutorial, you'll be introduced to the names for the different parts of a right triangle. Check it out!
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
- How Do You Solve for a Variable in Terms of Another Variable?
  
  Got an equation with two variables? Want to solve for one variable in terms of the other? Want to go the other way around? See how in this tutorial!
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
- What Does the Graph of the Sine Function Look Like?
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
- How Do You Graph a Translation of a Function?
  
  A great way to better understand how to translate a function is to practice! This tutorial takes you through the steps of graphing a function that's been translated up and to the right.
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
- What is the Sine Ratio?
  
  The sine ratio is a handy ratio when you're dealing with right triangles! In this tutorial, you'll learn what the sine ratio is and how to use it to find angle measurements in a right triangle.

What are the Trigonometric Cofunction Identities?

What are the Trigonometric Cofunction Identities?

Note:

Keywords:

Background Tutorials

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.