Definition OF Basic Emotions
Paul Ekman states that there are three meanings for the term "basic" . One of the meanings of "basic" is that there are a number of separate emotions that differ one from another in important ways.
The second meaning of the term "basic" is that emotions evolved for their adaptive value in dealing with fundamental life tasks. In this case fundamental life tasks means achievemnts, losses, frustrations, etc.
The third meaning of "basic" means to describe elements that combine to form more complex or compound emotions. For example, smugness might be considered to be a blend of the two elemental emotions, happiness and contempt.
According to Paul Ekman there are seven basic emotions  :
Robert Plutchik  considered eight primary emotions:
Plutchik proposed that baisc emotions are biologically primitive and have evolved in order to increase the reproductive fitness of the animal.
Plutchik argues for the primacy of these emotions by showing each to be the trigger of behaviour with high survival value, such as the way fear inspires the fight-or-flight response.
1 . Ekman, P. (1999). Basic Emotions. In T. Dalgleish and T. Power (Eds.) The Handbook of Cognition and Emotion P. 45-60. Sussex, U.K.: John Wiley & Sons, Ltd.
2 . Conversation with : Paul Ekman; The 43 Facial Muscles That Reveal Even the Most Fleeting Emotions. Judy Foreman. Retrieved July, 2010, from https://www.nytimes.com/2003/08/05/health/conversation-with-paul-ekman-43-facial-muscles-that-reveal-even-most-fleeting.html
3 . Robert Plutchik. Retrieved July, 2010, from https://en.wikipedia.org/wiki/Robert_Plutchik