**Basic Trigonometric Ratios Worksheet :**

Worksheet given in this section will be much useful for the students who would like to practice problems on basic trigonometric ratios.

Before look at the worksheet, if you would like to learn about basic trigonometric ratios,

**Problem 1 :**

In the right triangle PQR given below, find the basic trigonometric ratios of angle θ.

**Problem 2 :**

From the figure given below, find the basic trigonometric ratios of angle θ.

**Problem 3 :**

If sin θ = 13/85 and cos θ = 84/85, then find the values of tan θ and cos θ.

**Problem 4 :**

In triangle ABC, right angled at B, 15sin A = 12. Find the basic trigonometric ratios of angle A and angle C.

**Problem 1 :**

In the right triangle PQR given below, find the basic trigonometric ratios of the angle θ.

**Solution :**

In the triangle shown above, for the angle θ,

opposite side = 5

adjacent side = 12

hypotenuse = 13

Then, the basic trigonometric ratios of the angle θ are

sin θ = 5/13 cos θ = 12/13 tan θ = 5/12 |
csc θ = 13/5 sec θ = 13/12 cot θ = 5/12 |

**Problem 2 :**

From the figure given below, find the six trigonometric ratios of the angle θ.

In the triangle shown above, by Pythagorean Theorem,

AB^{2} = BC^{2} + CA^{2}

AB^{2} = 7^{2} + 24^{2}

AB^{2} = 49 + 576

AB^{2} = 625

AB^{2} = 25^{2}

AB = 25

In the triangle shown above, for the angle θ,

opposite side = 7

adjacent side = 24

hypotenuse = 25

Then, the basic trigonometric ratios of the angle θ are

sin θ = 7/25 cos θ = 24/25 tan θ = 7/24 |
csc θ = 25/7 sec θ = 25/24 cot θ = 24/7 |

**Problem 3 :**

If sin θ = 13/85 and cos θ = 84/85, then find the values of tan θ and cos θ.

**Solution : **

Finding the value of tan θ :

tan θ = sin θ / cos θ

tan θ = (13/85) / (84/85)

tan θ = (13/85) ⋅ (85/84)

tan θ = (13 ⋅ 85) / (85 ⋅ 84)

tan θ = 13/84

Finding the value of cot θ :

cot θ = 84/13

**Problem 4 :**

In triangle ABC, right angled at B, 15sin A = 12. Find the basic trigonometric ratios of angle A and angle C.

**Solution : **

**Given :** 15sin A = 12

Then,

15sin A = 12

Divide each side by 15.

sin A = 12/15 -----(1)

We know that,

sin A = opposite side / hypotenuse -----(2)

Comparing (1) and (2), we get

opposite side = 12

hypotenuse = 15

Let us consider the triangle ABC where right angled at B, with BC = 12 and AC = 15.

In the triangle shown above, by Pythagorean Theorem,

AC^{2} = AB^{2} + BC^{2}

15^{2} = AB^{2} + 12^{2}

225 = AB^{2} + 144

Subtract 144 from each side.

81 = AB^{2} + 144

9^{2} = AB^{2}

9 = AB

In the triangle shown above, for the angle A,

opposite side = 12

adjacent side = 9

hypotenuse = 15

Then, the basic trigonometric ratios of the angle A are

sin A = 12/15 = 4/5 cos A = 9/15 = 3/5 tan A = 12/9 = 4/3 |
csc A = 5/4 sec A = 5/3 cot A = 3/4 |

In the triangle shown above, for the angle C,

opposite side = 9

adjacent side = 12

hypotenuse = 15

Then, the basic trigonometric ratios of the angle C are

sin C = 9/15 = 3/5 cos C = 12/15 = 4/5 tan C = 9/12 = 3/4 |
csc C = 5/3 sec C = 5/4 cot C = 4/3 |

After having gone through the stuff given above, we hope that the students would have understood how to find the values of basic trigonometric ratios using right triangle.

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

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**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**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**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 **

**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 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**