The Curve $x = 5 - 10 \cos ^ { 2 } t , y = \tan t \left( 1 - 2 \cos ^ { 2 } t \right)$

question 45

Multiple Choice

The curve $x = 5 - 10 \cos ^ { 2 } t , y = \tan t \left( 1 - 2 \cos ^ { 2 } t \right)$ cross itself at some point $\left( x _ { 0 } , y _ { 0 } \right)$ . Find the equations of both tangent lines at that point.

• A) \(y = \frac { x } { 5 } , y = - \frac { x } { 10 }\)
• B)
• \(y = \frac { x } { 2 } - 10 , y = - \frac { x } { 2 } - 2\)
• C) \(y = x + 5 , y = - x + 5\)
• D)
• \(y = \frac { x } { 2 } , y = - \frac { x } { 2 }\)
• E)
• \(y = \frac { x } { 2 } + 8 , y = - \frac { x } { 2 } + 2\)

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Definitions:

Divergent Thinking

Type of thinking in which a person starts from one point and comes up with many different ideas or possibilities based on that point.

Circular Thinking

A form of reasoning in which the conclusion is also used as one of the premises, often leading to logical fallacies.

Convergent Thinking

Type of thinking in which a problem is seen as having only one answer, and all lines of thinking will eventually lead to that single answer, using previous knowledge and logic.

Morphemes

The smallest grammatical units in a language that carry meaning.