What is the value of tan^2(-pi/4) ?

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tan^2(-pi/4)

tan^{2} (- \frac{π}{4})

1

Solution steps

tan^{2} (- \frac{π}{4})

Rewrite using trig identities:

tan (- \frac{π}{4}) = - 1

tan (- \frac{π}{4})

Use the following property:

tan (- x) = - tan (x)

tan (- \frac{π}{4}) = - tan (\frac{π}{4})

= - tan (\frac{π}{4})

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= - 1

= (- 1)^{2}

Simplify

(- 1)^{2} : 1

(- 1)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 1)^{2} = 1^{2}

= 1^{2}

Apply rule

1^{a} = 1

= 1

= 1

8 sin (\frac{π}{6}) cos (\frac{π}{3})

cos (ln (2))

sin (- 25 5^{\circ})

sin (5 \cdot \frac{π}{2})

arccos (\frac{2.9}{3.2})