Find the slopes of the lines which make the following angles with the positive direction of x-axis:

$(i) - \frac{π}{4} (i i) \frac{2 π}{3} (i i i) \frac{3 π}{4} (i v) \frac{π}{3}$

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Solution

$(i) Angle made with positive x axis is - \frac{π}{4} ∴ m = t a n θ = t a n (\frac{- π}{4}) = - 1 (ii) Angle made with positive x axis is \frac{2 π}{3} ∴ m = t a n θ = t a n (\frac{2 π}{3}) = - \sqrt{3} (iii) Angle made with positive x axis is \frac{3 π}{4} ∴ m = t a n θ = t a n (\frac{3 π}{4}) = t a n (π - \frac{π}{4}) = - 1 (iv) Angle made with positive x axis is \frac{π}{3} ∴ m = t a n θ = t a n (\frac{π}{3}) = \sqrt{3}$

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Similar questions

- \frac{π}{4}

\frac{2 π}{3}

\frac{3 π}{4}

\frac{π}{3}

If the line makes angle $\frac{π}{6}$ and $\frac{π}{3}$ with positive direction of x and y axes respectively, then it makes with z-axis is

θ (\neq π / 2)

x - a x i s

s i n^{- 1} (s i n \frac{2 π}{3}) = \frac{2 π}{3}

t a n^{- 1} (t a n \frac{2 π}{3}) = \frac{- π}{3}

c o s^{- 1} (c o s \frac{2 π}{3}) = \frac{2 π}{3}

s e c^{- 1} (s e c \frac{5 π}{4}) = \frac{3 π}{4}

s i n^{- 1} (s i n \frac{2 π}{3}) = \frac{2 π}{3}

t a n^{- 1} (t a n \frac{2 π}{3}) = \frac{- π}{3}

c o s^{- 1} (c o s \frac{2 π}{3}) = \frac{2 π}{3}

s e c^{- 1} (s e c \frac{5 π}{4}) = \frac{3 π}{4}

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