Trigonometric Ratios for 60 Degrees: Value for the Trigonometrical Ratios for certain angle such as ,, and are commonly called standard angles and the trigonometrical ratios of these angles are frequently used to solve particular angles. In this section we will derive the value of trigonometric ratios for .
Consider an equilateral with each side = 2a units We know that each angle of Moreover in an equilateral triangle the altitude and median coincide. From A, draw As AD is the median also therefore D is the mid - point of BC, As BC = 2a units BD = DC = a units Also, [ AD is perpendicular BC ] and [ Each angle in equilateral triangle is ] Therefore in triangle ABD [Angle Sum Property] |
Now is a right angled triangle so by pythagorous theorem
Substituting the value of AB and BD
In right we have
Thus, we have
sin A | cos A | tan A | cosec A | sec A | cot A | |
2 |
Illustration: Simplify the given expression
Solution: To solve this expression we will substitute the value of the ratios at
If ,then | |||
Right Option : D | |||
View Explanation |
Solve the following expression: | |||
Right Option : D | |||
View Explanation |
is equal to ___________________. | |||
Right Option : C | |||
View Explanation |
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