Trigonometry Values

Trigonometry values are all about the study of triangles. The word ‘Trigon’ means triangle and ‘metry’ means ‘measurement’. Trigonometry values of trigonometric ratios deal with the measurement of lengths and angles of the right-angle triangle. The values of trigonometric ratios for 00, 300, 450, 600 and 900 are commonly used to solve trigonometry problems.

Let us learn more about trigonometry values and trigonometric formulas in this article.

Values of Trigonometry Ratios

Let us learn, trigonometry values for all the ratios, i.e. sin, cos, tan, cot, sec, cosec, taking an example of the right-angle triangle.

trigonometry values

Suppose ABC is a right angled triangle, right angled at B. This triangle has a hypotenuse AC, an adjacent side AB which is adjacent to angle θ and a perpendicular BC opposite to Angle θ.

Trigonometry values are based on three major trigonometric ratios, Sine, Cosine and Tangent.

Sine or sinθ= \(\frac{Side opposite to θ}{Hypotenuse}\)=\(\frac{BC}{AC}\)

Cosines or cosθ= \(\frac{Adjacent side to θ}{Hypotenuse}\)=\(\frac{AB}{AC}\)

Tangent or tanθ= \(\frac{Side opposite to θ}{Adjacent side to θ}\)=\(\frac{BC}{AB}\)

Similarly, we can write the trigonometric values for Reciprocal properties, Sec, Cosec and Cot ratios.

Secθ = 1/Cosθ = \(\frac{Hypotenuse}{Adjacent side to angleθ}\) = \(\frac{AC}{AB}\)

Cosecθ = 1/Sinθ = \(\frac{Hypotenuse}{Side opposite to angle θ}\) = \(\frac{AC}{BC}\)

Cotθ = 1/tanθ = \(\frac{Adjacent side to angle θ}{Side opposite to angleθ}\)=\(\frac{AB}{BC}\)

Also,

Secθ .Cosθ =1

Cosecθ .Sinθ =1

Cotθ .Tanθ =1

Let us draw a table to define trigonometric values for all ratios:

Angle

00

300

450

600

900

Sinθ

0

1/2

\(1/\sqrt{2}\) \(\sqrt{3}/2\)

1

Cosθ

1

\(\sqrt{3}/2\) \(1/\sqrt{2}\)

1/2

0

Tanθ

0

\(1/\sqrt{3}\)

1

\(\sqrt{3}\)

Cotθ

\(\sqrt{3}\)

1

\(1/\sqrt{3}\)

0

Secθ

1

\(2/\sqrt{3}\) \(\sqrt{2}\)

2

Cosecθ

2

\(\sqrt{2}\) \(2/\sqrt{3}\)

1

We can also use below given formulas to find the values of trigonometry ratios;

Tanθ = \(\frac{sin\theta}{cos\theta }\)

Cotθ = \(\frac{cos\theta}{sin\theta }\)

Sinθ = \(\frac{tan\theta}{cos\theta }\)

Cosθ = \(\frac{sin\theta}{tan\theta }\)

Secθ = \(\frac{tan\theta}{sin\theta }\)

Cosecθ = \(\frac{cos\theta}{tan\theta}\)

Also,

Sin(90-θ)=Cosθ

Cos(90-θ)=Sinθ

Tan(90-θ)=Cotθ

Cot(90-θ)=Tanθ

Sec(90-θ)=Cosecθ

Cosec(90-θ)=Secθ

Problem: Find the value of sin(90-45)0.

Solution: sin(90-45)0 = cos 450 = \(1/\sqrt{2}\)

Problem: If tan θ = 4 and sin θ = 6. Then find the value of cos θ.

Solution: We know, cosθ = \(\frac{sin\theta}{tan\theta }\)

Therefore, cosθ = 6/4 = 3/2

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Practise This Question

In ΔABC and ΔPQR, AB = 4 cm, BC = 5 cm, AC = 6 cm and PQ = 4 cm, QR = 5 cm, PR = 6 cm, then