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Write each function in terms of its cofunction . PowerPoint PPT Presentation


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WARM-UP. Write each function in terms of its cofunction. (a)cos 48 °. = sin (90 ° – 48°) = sin 42°. (b)tan 67 °. = cot (90 ° – 67°) = cot 23°. (c)sec 44 °. = csc (90 ° – 44°) = csc 46°. ID/Quadratic Quiz. Write all identities Pythagoreans (3) Quotients (2) Cofunctions (6)

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Write each function in terms of its cofunction

WARM-UP

Write each function in terms of its cofunction.

(a)cos 48°

= sin (90° – 48°) = sin 42°

(b)tan 67°

= cot (90° – 67°) = cot 23°

(c)sec 44°

= csc (90° – 44°) = csc 46°


Id quadratic quiz

ID/Quadratic Quiz

Write all identities

  • Pythagoreans (3)

  • Quotients (2)

  • Cofunctions (6)

  • Reciprocal (6)

    Solve the quadratics

    5. x2 + 11x + 24 = 0

    6. (x – 3)2 – 4 = 0

    7. Write the quadratic formula.


Write each function in terms of its cofunction

Trig Game PlanDate: 9/24/13


Increasing decreasing functions

Increasing/Decreasing Functions

As A increases, y increases and x decreases.

Since r is fixed,

sin A increases

csc A decreases

cos A decreases

sec A increases

tan A increases

cot A decreases


Write each function in terms of its cofunction

COMPARING FUNCTION VALUES OF ACUTE ANGLES

Example 1a

Determine whether each statement is true or false.

(a) sin 21° > sin 18° (b) cos 49° ≤ cos 56°

(a)In the interval from 0 to 90, as the angle increases, so does the sine of the angle, which makes sin 21° > sin 18° a true statement.

(b)In the interval from 0 to 90, as the angle increases, the cosine of the angle decreases, which makes cos 49° ≤ cos 56° a false statement.


Write each function in terms of its cofunction

COMPARING FUNCTION VALUES OF ACUTE ANGLES

Example 1b

  • Determine whether each statement is true or false.

(a)tan 25° < tan 23°

In the interval from 0° to 90°, as the angle increases, the tangent of the angle increases.

tan 25° < tan 23° is false.

(b)csc 44° < csc 40°

In the interval from 0° to 90°, as the angle increases, the sine of the angle increases, so the cosecant of the angle decreases.

csc 44° < csc 40° is true.


30 60 90 triangles

30°- 60°- 90° Triangles

Bisect one angle of an equilateral to create two 30°-60°-90° triangles.


30 60 90 triangles1

30°- 60°- 90° Triangles

Use the Pythagorean theorem to solve for x.


Write each function in terms of its cofunction

FINDING TRIGONOMETRIC FUNCTION VALUES FOR 60°

Example 2

Find the six trigonometric function values for a 60° angle.


Write each function in terms of its cofunction

FINDING TRIGONOMETRIC FUNCTION VALUES FOR 60° (continued)

Example 2

Find the six trigonometric function values for a 60° angle.


45 45 right triangles

45°- 45° Right Triangles

Use the Pythagorean theorem to solve for r.


45 45 right triangles1

45°- 45° Right Triangles

adjacent


45 45 right triangles2

45°- 45° Right Triangles


Function values of special angles

Function Values of Special Angles

sin 

cos 

tan 

cot 

sec 

csc 

30

45

60


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