# EVALUATING TRIGONOMETRIC FUNCTIONS OF SPECIAL ANGLES WORKSHEET

## About "Evaluating trigonometric functions of special angles worksheet"

Evaluating trigonometric functions of special angles worksheet :

Here we are going to see some practice questions on evaluating trigonometric functions of special angles.

## Evaluating trigonometric functions of special angles worksheet - Practice questions

(1)  Evaluate sin 45° + cos 45°

(2)  Evaluate sin 60° tan 30°

(3)  Evaluate tan 45°/(tan 30° + tan 60°)

(4)  Evaluate tan2 60° - 2tan2 45° - cot2 30° + 2sin2 30°

(5)  Evaluate 4 (sin30° + cos460°) - 3 (cos245° - sin290°)

(6)  Evaluate 6 cos290° + 3 sin290° + 4 tan245°

(7)  Evaluate 4 cot245  - sec260 + sin260 + cos260

(8)  Evaluate sin 30°cos 60° + cos 30° sin 60°

## Evaluating trigonometric functions of special angles worksheet - Solution

Question 1 :

Evaluate sin 45° + cos 45°

Solution :

sin 45°  =  1/√2

cos 45°  =  1/√2

sin 45° + cos 45°  =  (1/√2)  +  (1/√2)

=  (1 + 1)/√2

=  2/√2

=  (√2 ⋅ √2) / √2

=  √2

Question 2 :

Evaluate sin 60° tan 30°

Solution :

sin 60°  =  √3/2

tan 30°  =  1/√3

sin 60° cos 30°  =  (√3/2)  (1/√3)

=  1/2

Question 3 :

Evaluate tan 45°/(tan 30° + tan 60°)

Solution :

tan 45°  =  1

tan 30°  =  1/2

tan 60°  =  √3

tan 45°/(tan 30° + tan 60°)  =  1/[(1/√3) + √3]

=  1/[(1 + 3)/√3]

=  √3/4

Example 4 :

Evaluate tan2 60° - 2tan2 45° - cot2 30° + 2sin2 30

Solution :

tan60°  =  (tan 60°)2   =  (√3) =  3

tan45°  =  (tan 45°)2   =  (1) =  1

cot30°  =  (cot 30°)2   =  (√3) =  3

sin30°  =  (sin 30°)2   =  (1/2) =  1/4

=  3 - 2 (1) - 3 + 2(1/4)

=  -2 + 1/2

=  (-4 + 1)/2  =  -3/2

Question 5 :

Evaluate 4 (sin30° + cos460°) - 3 (cos245° - sin290°)

Solution :

sin30°  =  (sin 30°)4   =  (1/2) =  1/16

cos4 60°  =  (cos 60°)4   =  (1/2) =  1/16

cos45°  =  (cos 45°)2   =  (1/2) =  1/2

sin90°  =  (sin 90°)2   =  (1) =  1

=  4 [(1/16) + (1/16)] - 3[(1/2) - 1]

=  4(2/16)  -  3 (-1/2)

=  (1/2) + (3/2)

=  (1 + 3)/2  =  4/2  = 2

Question 6 :

Evaluate 6 cos290° + 3 sin290° + 4 tan245°

Solution :

cos290°  =  (cos 90°)=  (0)2  =  0

sin290°  =  (sin 90°)2  =  (1)2  =  1

tan245°  =  (tan 45°)2  =  (1)2  =  1

6 cos290° + 3 sin290° + 4 tan245°  =  6(0) + 3(1) + 4(1)

=  0 + 3 + 4

=   7

Question 7 :

Evaluate 4 cot245  - sec260 + sin260 + cos260

Solution :

cot245°  =  (cot 45°)2  =  (1)2  =  1

sec260  =  (sec 60°)2  =  (2)2  =  4

sin260  =  (sin 60°)2  =  (√3/2)2  =  3/4

cos260  =  (cos 60°)2  =  (1/2)2  =  1/4

=  4(1) - 4 + (3/4) + (1/4)

=  4 - 4 + (3+1)/4

=  4/4  =  1

Question 8 :

Evaluate sin 30°cos 60° + cos 30° sin 60°

Solution :

sin 30°  =  1/2

cos 60°  =  1/2

cos 30°  =  √3/2

sin 60°  =  √3/2

=  (1/2) (1/2) + (√3/2)(√3/2)

=  (1/4) + (3/4)

=  (1 + 3)/4

=  4/4

=  1

After having gone through the stuff given above, we hope that the students would have understood "Evaluating trigonometric functions of special angles worksheet".

Apart from the stuff given above, if you want to know more about "Evaluating trigonometric functions of special angles worksheet"

Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6